Mathematics Class IX Questions Bank

Question 1 of 40

1. Question
1 point(s)
The radius of a sphere and the edge of a cube are equal. The ratio of the their volume is :
- $4\pi:3 $
- $4:3 $
- $3:4 $
- $4\pi:1 $
Correct

Incorrect

Hint

Volume of sphere $=\dfrac{4}{3}\pi r^3$
Volume of cube $a^3=r^3$
Ratio $=\dfrac{\dfrac{4}{3}\pi r^3}{r^3}=\dfrac{4}{3}\pi :1\\ \\ =4\pi:3$
Question 2 of 40

2. Question
1 point(s)
27 solid iron spheres each of radius r, are melted to form a new sphere. The radius of the new sphere is :
- 2r
- 3r
- 4r
- 7r
Correct

Incorrect

Hint

$27\times\left(\dfrac{4}{3}\pi r^3\right)=\dfrac{4}{3}\pi (r^1)^3\\ \\ 27r^3=r^{1^3}\\ \\ r^{1^3}=(3r)^3\Rightarrow r^1=3r$
Question 3 of 40

3. Question
1 point(s)
The diameters of two cones are equal. If their slant height are in the ratio 7 : 8, then the ratio of their curved surface areas will be
- 2 : 3
- 5 : 6
- 4 : 5
- 7 : 8
Correct

Incorrect

Hint

$\dfrac{\pi rl_1}{\pi r l_2}=\dfrac{l_1}{l_2}=\dfrac{7}{8}$
Question 4 of 40

4. Question
1 point(s)
The radius of a wire is decreased to one thrid. If the volume remains the same, its length will increase by :
- 2 times
- 3 times
- 6 times
- 9 times
Correct

Incorrect

Hint

original volume $=\pi r^2h$
New volume $=\pi\left(\dfrac{r}{3}\right)^2 H$
A/Q $\pi r^2h=\pi\left(\dfrac{r}{3}\right)^2H$
$H=9h$
Question 5 of 40

5. Question
1 point(s)
The volumes of two spheres are in the ratio 64 : 27. The ratio of their radii is equal to :
- 4 : 3
- 3 : 4
- 16 : 9
- 16 : 27
Correct

Incorrect

Hint

$\dfrac{\dfrac{4}{3}\pi r^3_1}{\dfrac{4}{3}\pi r^3_2}=\dfrac{64}{27}\Rightarrow \left(\dfrac{r_1}{r_2}\right)^3=\left(\dfrac{4}{3}\right)^3\\ \\ \Rightarrow \dfrac{r_1}{r_2}-\dfrac{4}{3}$
Question 6 of 40

6. Question
1 point(s)
How many bricks, each measuring $50\ cm \times 25\ cm \times 12\ cm$, will be needed to build a wall measuring $16m \times 12 m \times 45cm$ ?
- 4860
- 5760
- 6320
- 8120
Correct

Incorrect

Hint

Number of bricks $=\dfrac{1600\times1200\times45}{50\times25\times12}\\ \\ =36\times160=5760$
Question 7 of 40

7. Question
1 point(s)
If the slant height of a cone is double its base radius,then volume of the cone is :
- $\dfrac{1}{\sqrt3}\pi\ \text{(radius)}^3 $
- $\sqrt3\pi\ \text{(radius)}^3 $
- $\pi\ \text{(radius)}^3 $
- $2\pi\ \text{(radius)}^3 $
Correct

Incorrect

Hint

Volume of the cone $=\dfrac{1}{3}\pi r^2h$
$l=2r\ \ l^2=r^2+h^2\\ \\ 4r^2=r^2+h^2\Rightarrow h^2=3r^2\\ \\ \Rightarrow h=\sqrt3r\\ \\ V=\dfrac{1}{3}\pi r^2\times\sqrt3r=\dfrac{1}{\sqrt3}\pi (r^3)$
Question 8 of 40

8. Question
1 point(s)
A cuboid has 12 edges. The combined length of all 12 edges of the cuboid is equal to :
- length $\times $ breadth $\times $ height
- 4 $\times $ (length $\times $ breadth $\times $ height)
- 4 $\times $ (length + breadth + height)
- 3 $\times $ (length + breadth + height)
Correct

Incorrect

Hint

In any cuboid , 4 edges = l, 4 edges = b, 4 edges = h
Total length = 4l + 4b + 4h = 4(l+b+h)
Question 9 of 40

9. Question
1 point(s)
The area of the iron sheet required to prepare a cone without base of height 3 cm with radius 4 cm is :
- $\dfrac{440}{7}cm^2 $
- $400\ cm^2 $
- $\dfrac{400}{7}cm^2 $
- $\dfrac{7}{440}cm^2 $
Correct

Incorrect

Hint

$l=\sqrt{3^2+4^2}=\sqrt{25}=5$
Area of iron sheet $=\pi rl=\dfrac{22}{7}\times4\times5$
$=\dfrac{440}{7}\ cm^2$
Question 10 of 40

10. Question
1 point(s)
Curved surface area of a right circular cylinder is $8.8\ m^2$. If the radius of the base of the cylinder is $1.4\ m$, its height is equal to :
- 10 m
- 100 m
- 0.1 m
- 1 m
Correct

Incorrect

Hint

CSA of cylinder $=2\pi rh$
$8.8=2\times\dfrac{22}{7}\times1.4\times h\\ \\ \Rightarrow h=\dfrac{8.8\times7}{2\times22\times1.4}=\dfrac{61.6}{61.6}=1m$
Question 11 of 40

11. Question
1 point(s)
The height (h) of a cone is equal to its base diameter (2 r). The slant height of the cone is :
- $\sqrt{r^2+h^2} $
- $r\sqrt5 $
- $h\sqrt5 $
- $rh\sqrt5 $
Correct

Incorrect

Hint

$l=\sqrt{r^2+h^2}=\sqrt{r^2+(2r)^2}\\ \\ =\sqrt{r^2+4r^2}=\sqrt{5r^2}\\ \\ =\sqrt{5}r$
Question 12 of 40

12. Question
1 point(s)
The volume of the largest cone which can be cut from a cube of edge a is :
- $\dfrac{\pi a^2}{12} $
- $\dfrac{\pi a^3}{3} $
- $\pi a^3 $
- $\dfrac{\pi a^3}{12} $
Correct

Incorrect

Hint

Radius $=\dfrac{a}{2}$ , height $=a$
Volume $=\dfrac{1}{3}\pi r^2h=\dfrac{1}{3}\pi\left(\dfrac{a}{2}\right)^2\times a$
$=\dfrac{1}{3}\pi\dfrac{a^2\times a}{4}=\dfrac{\pi a^3}{12}$
Question 13 of 40

13. Question
1 point(s)
If the volume of a cube is $3\sqrt3\ a^3 $, then surface area of the cube is :
- $6a^2 $
- $\sqrt3\ a^2 $
- $18a^2 $
- $18\sqrt3\ a^2 $
Correct

Incorrect

Hint

$x^3=3\sqrt3a^3\\ \\ x^3=(\sqrt3a)^3\ \Rightarrow x=\sqrt3a$
Total surface area $=6x^2=6\times(\sqrt3a)^2$
$=6\times3a^2=18a^2$
Question 14 of 40

14. Question
1 point(s)
The lateral surface area of a cube is $256\ m^2 $. The volume of the cube is :
- $512\ m^3 $
- $64\ m^3 $
- $216\ m^3 $
- $256\ m^3 $
Correct

Incorrect

Hint

$4a^2=256\Rightarrow a^2=\dfrac{256}{4}=64\Rightarrow a=8$
Volume $=a^3=8^3=512\ m^3$
Question 15 of 40

15. Question
1 point(s)
The number of planks of dimensions $(4m \times 5m \times 2m)$ that can be stored in a pit which is $40m$ long, $12\ m$ wide and $160\ m$ deep is :
- 1900
- 1920
- 1800
- 1840
Correct

Incorrect

Hint

Number of planks $=\dfrac{40\times12\times160}{4\times5\times2}=1920$
Question 16 of 40

16. Question
1 point(s)
The length of the longest pole that can be put in a room of dimensions $(10m \times 10m \times 5m)$ is :
- 15 m
- 16 m
- 10 m
- 12 m
Correct

Incorrect

Hint

length of the largest pole $=\sqrt{10^2+10^2+5^2}=\sqrt{100+100+25}=\sqrt{225}=15\ m$
Question 17 of 40

17. Question
1 point(s)
In a cylinder, if radius is halved and height is doubled, the volume will be :
- Same
- Doubled
- Halved
- Four times
Correct

Incorrect

Hint

Volume of cylinder $=\pi r^2h$
Volume of new cylinder $=\pi\left(\dfrac{r}{2}\right)^2\times 2h$
$=\pi\times\dfrac{r^2}{4}\times 2h=\dfrac{\pi r^2h}{2}$
Question 18 of 40

18. Question
1 point(s)
If the radius of a wire is decreased to one–fourth of its original and its volume remains same, then how many times will the new length become of its original length ?
- 4 times
- 8 times
- 16 times
- 20 times
Correct

Incorrect

Hint

Volume of wire $=\pi r^2l$
New radius $=\dfrac{1}{4}r$
A/Q $\pi r^2l=\pi \left(\dfrac{lr}{4}\right)^2l'$
$\Rightarrow l'=16l$
Question 19 of 40

19. Question
1 point(s)
Five cubes each of edge 1 cm are joined face to face. The surface area of the cuboid thus formed is
- $5\ cm^2 $
- $10\ cm^2 $
- $11\ cm^2 $
- $22\ cm^2 $
Correct

Incorrect

Hint

$l=5\times1=5,\ b=1,\ h=1$
Surface area $=2(lb+bh+hl)$
$2(5+l+b)=2\times11=22\ cm$
Question 20 of 40

20. Question
1 point(s)
If the radius of a cone is increased by 100% and height is decreased by 50%, then the volume of the new cone is …………….. the volume of the original cone.
- Twice
- Thrice
- Half
- Unchanged
Correct

Incorrect

Hint

Volume of cone $=\dfrac{1}{3}\pi r^2h$
$r^1=r+\dfrac{100}{100}r=2r\\ \\ h^1=h-\dfrac{50h}{100}=\dfrac{h-h}{2}=\dfrac{h}{2}$
Volume $=\dfrac{1}{3}\pi (2r)^2\times\dfrac{h}{2}=\dfrac{1}{3}\times\pi\times4r^2\times\dfrac{h}{2}\\ \\ =\dfrac{1}{3}\pi\times2r^2\times h$
Question 21 of 40

21. Question
1 point(s)
Two cubes each of edge 5 cm are joined face to face. The surface area of the cuboid thus formed is equal to :
- $200\ cm^2 $
- $250\ cm^2 $
- $360\ cm^2 $
- $280\ cm^2 $
Correct

Incorrect

Hint

$l=5+5=10\ cm,\ b=5\ cm,\ h=5\ cm$
Surface area $=2(lb+bh+hl)$
$=2(50+25+50)\\ \\ =2\times125=250\ cm^2$
Question 22 of 40

22. Question
1 point(s)
If the radius of a sphere is increased by $5\ cm$, then its surface area increases by $704\ cm^2$. The radius of the sphere before the increase was :
- 2.1 cm
- 3.1 cm
- 4.1 cm
- 5.1 cm
Correct

Incorrect

Hint

$4\pi(r+5)^2=4\pi r^2+704\\ \\ 4\pi r^2+40\pi r+100\pi=4\pi r^2+704\\ \\ 40\pi r+100\pi=704\\ \\ \dfrac{22}{7}\times(40r+100)=704\\ \\ 40r+100=124\\ \\ \Rightarrow r=3.1\ cm$
Question 23 of 40

23. Question
1 point(s)
A heap of wheat is in the form of a cone whose radius is 3 m and slant height is 7 m. The heap is to be covered by canvas to protect it from rain. The area of canvas required is :
- $50\ m^2 $
- $60\ m^2 $
- $66\ \pi\ m^2 $
- $66\ m^2 $
Correct

Incorrect

Hint

Area of canvas $=\pi rl$
$=\dfrac{22}{7}\times3\times7=66 \ m^2$
Question 24 of 40

24. Question
1 point(s)
A rectangular sheet of paper $22\ cm \times 15\ cm$ is rolled along its length to form a hollow cylinder. The radius of the cylinder is :
- 7 cm
- 15 cm
- 11 cm
- 3.5 cm
Correct

Incorrect

Hint

$2\pi r=22\\ \\ 2\times\dfrac{22}{7}\times r=22\\ \\ r=3.5\ cm$
Question 25 of 40

25. Question
1 point(s)
A cylinder and a cone have the same base radius. If their volumes are equal, then ratio of their heights is :
- 2 : 1
- 1 : 2
- 1 : 3
- 1 : 4
Correct

Incorrect

Hint

$\dfrac{V_1}{V_2}=\dfrac{\pi r^2h_1}{\dfrac{1}{3}\pi r^2h_2}\\ \\ =\dfrac{1}{3}h_2=h_1\\ \\ \dfrac{h_1}{h_2}=\dfrac{1}{3}$
Question 26 of 40

26. Question
1 point(s)
The thickness of a hollow cylinder is 1 cm. It is 7 cm long and its inner radius is 3 cm. The volume of the wood required to make the cylinder is :
- $154\ \pi\ cm^3 $
- $514\ cm^3 $
- $154\ cm^3 $
- $145\pi\ cm^3 $
Correct

Incorrect

Hint

Volume of outer cylinder $=\dfrac{2\pi}{7}\times4\times4\times7$
$=112\pi \ cm^3=\dfrac{112\times22}{7}=352$
Volume of inner cylinder $=\pi\times3\times3\times7$
$=63\pi\ cm^3\\ \\ =63\times\dfrac{22}{7}=198$
Volume of wood $=154\ cm^3$
Question 27 of 40

27. Question
1 point(s)
The total surface area of a cone whose radius is $\dfrac{r}{2} $ and slat height $2l $ is :
- $2\pi r\ (1+r) $
- $\pi r\left(l+\dfrac{r}{4}\right) $
- $\pi r\ (1+r) $
- $2\pi rl $
Correct

Incorrect

Hint

$\pi rl+\pi r^2=\pi\times\dfrac{r\times 2l}{2}+\pi\times \left(\dfrac{r}{2}\right)^2\\ \\ =\pi rl^2+\dfrac{\pi r^2}{4}\\ \\ =\pi r\left(l+\dfrac{r}{4}\right)$
Question 28 of 40

28. Question
1 point(s)
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is :
- 1 : 4
- 1 : 3
- 2 : 3
- 2 : 1
Correct

Incorrect

Hint

$r_1=6,\ r_2=12\\ \\ \dfrac{r_1^2}{r_2^2}=\dfrac{3\pi r_1^2}{3\pi r^2_2}=\dfrac{6^2}{12^2}=\dfrac{36}{144}=\dfrac{1}{4}$
Question 29 of 40

29. Question
1 point(s)
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is :
- 4.2 cm
- 2.1 cm
- 2.4 cm
- 1.6 cm
Correct

Incorrect

Hint

Volume of cone $=\dfrac{1}{3}\times\dfrac{22}{7}\times2.1\times2.1\times8.4$
$=38.808\ cm^3$
A/Q $\dfrac{4}{3}\pi r^3=38.808$
$r^3=9.261\Rightarrow r=2.1\ cm$
Question 30 of 40

30. Question
1 point(s)
Base area of a cylinder is 154 sq cm. Its height is 5 cm. Then its volume is :
- 308 cubic cm
- 770 cubic cm
- 525 cubic cm
- 600 cubic cm
Correct

Incorrect

Hint

Volume of cylinder $=\pi r^2h$
$154\times5=770\ cm^3$
Question 31 of 40

31. Question
1 point(s)
The total surface area of a cone whose radius is $2r $ and slant height $\dfrac{l}{2} $ is:
- $2\pi r\ (l + r) $
- $2\pi r\left(\dfrac{l }{2}+r\right) $
- $2\pi r\ (l+4r) $
- $\pi r\ (l+4r) $
Correct

Incorrect

Hint

TSA of a cone $=\pi rl+\pi r^2$
$=\pi\times(2r)\times\dfrac{l}{2}+\pi(2r)^2\\ \\ =\pi rl+\pi\times 4r^2\\ \\ =\pi r(l+4r)$
Question 32 of 40

32. Question
1 point(s)
Diameter of the earth is four times (approximately) the diameter of the moon, then the ratio of their surface areas is :
- 4 : 1
- 8 : 1
- 16 : 1
- 64 : 1
Correct

Incorrect

Hint

$D=4d\ \Rightarrow\ R=4r\\ \\ \dfrac{4\pi R^2}{4\pi r^2}=\dfrac{4\pi (4r)^2}{4\pi r^2}=\dfrac{16r^2}{r^2}=\dfrac{16}{1}$
Question 33 of 40

33. Question
1 point(s)
Curved surface area of a hemisphere of diameter 2r is :
- $2\pi r^2 $
- $3\pi r^2 $
- $4\pi r^2 $
- $8\pi r^2 $
Correct

Incorrect

Hint

Radius $=r\ cm$
CSA of hemisphere $=2\pi r^2$
Question 34 of 40

34. Question
1 point(s)
In a cylinder, radius is doubled and height is halved. The curved surface area will be :
- Halved
- Doubled
- Same
- Four times
Correct

Incorrect

Hint

CSA of a cylinder $=2\pi rh$
$=2\pi\times2r\times\dfrac{h}{2}\\ \\ =2\pi rh$
Question 35 of 40

35. Question
1 point(s)
A cuboid has dimensions $5\ cm \times 4\ cm \times 2\ cm$. Number of cubes of $2\ cm$ side that can be cut from the cuboid is :
- 18
- 5
- 10
- None of these
Correct

Incorrect

Hint

Number of cubes $=\dfrac{5\times4\times2}{2\times2\times2}=5$
Question 36 of 40

36. Question
1 point(s)
The length of the longest rod that can be put in a hall of dimension $23\ m \times 10\ m \times 10\ m$ is :
- 20 m
- 15 m
- 23 m
- 27 m
Correct

Incorrect

Hint

length of the longest rod
$=\sqrt{(23)^2+(10)^2+(10)^2}\\ \\ =\sqrt{529+200}=\sqrt{729}=27\ m$
Question 37 of 40

37. Question
1 point(s)
The area of the base of a solid hemisphere is $36\ cm^2$. Its curved surface area is :
- $36\ cm^2 $
- $72\ cm^2 $
- $108\ cm^2 $
- $98\ cm^2 $
Correct

Incorrect

Hint

CSA $=2\pi r^2$
$=2\times36\\ \\ =72\ cm^2$
Question 38 of 40

38. Question
1 point(s)
The curved surface area of a cylinder is 2200 sq cm and circumference of its base is 220 cm. Then the height of the cylinder is :
- 22 cm
- 10 cm
- 5 cm
- 2.2 cm
Correct

Incorrect

Hint

CSA of cylinder $=2\pi rh$
$\Rightarrow 2200=220\times h\\ \\ \Rightarrow h=\dfrac{2200}{220}=10\ cm$
Question 39 of 40

39. Question
1 point(s)
The lateral surface area of a cube is $100\ m^2 $. The volume of the cube is :
- $1000\ m^3 $
- $100\ m^3 $
- $25\ m^3 $
- $125\ m^3 $
Correct

Incorrect

Hint

$4a^2=100\ \Rightarrow a^2=25\Rightarrow a=5\ m$
Volume $=a^3=5^3=125\ m^3$
Question 40 of 40

40. Question
1 point(s)
The curved surface area of a hemisphere is $77\ cm^2 $. Radius of the hemisphere is
- 3.5 cm
- 7 cm
- 10.5 cm
- 11 cm
Correct

Incorrect

Hint

$2\pi r^2=77\\ \\ 2\times\dfrac{22}{7}\times r^2=77\ \Rightarrow\ r^2=\dfrac{7\times77}{2\times22}\\ \\ r^2=\dfrac{49}{4}\Rightarrow r=\dfrac{7}{2}=3.5\ cm$