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A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.
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Volume of cone
Volume of hemisphere
Volume of cylinder
A semicircular sheet of iron of diameter 28 cm is bent into an open conical cup. Find the capacity of the cup.
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capacity of conical cup
If the length of the diagonal of cube is \(6\sqrt3\ cm \), find hte edge of the cube.
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Length of the diagonal of a cube
The volume of a sphere is equal to twoโthirds of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere. Is this state ment true ? Justify your answer.
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True
Volume of sphere Volume of cylinder
An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then find the volume of the cone.
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radius , height
Volume of a cone
If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere ?
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Volume of first sphere
Volume of second
Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 2 r.
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Radius of the cone
Height of the cone
Volume
A sphere is inscribed in a cube. Find the ratio of the volume of the cube to the volume of the sphere.
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Volume of cube
Radius of sphere
Volume of sphere
Check whether the following statement is true or not, If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.
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False
Volume
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
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For sphere ,
For cylindrical wire ,
A/Q
Volume of cylinder = Volume of sphere
Find the amount of water displaced by a solid spherical ball of diameter 28 cm. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Amount of water displaced = Volume of sphere
Volume
Curved surface area of a right circular cylinder is \(4.4\ m^2 \). If the radius of the base of the cylinder is \( 0.7\ m\), find its height. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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A solid cube of side 12 cm is cut into eight cubes of equal volumes. What will be the side of a new cube?Also, find the ratio between their surface area.
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Ratio of their surface area
The curved surface area of a right circular cylinder of height \(14\ cm \) is \(88\ cm^2 \). Find the volume of the cylinder. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of the cylinder
The circumference of the base of 9 m high wooden solid cone is 44 m. Find its volume. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of cone
The radius and height of a cylinder are in the ratio 2 : 3. If the volume of the cylinder is \(1617\ cm^3 \), find its height. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of cylinder
Height
A semi – circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of the cup.
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capacity of conical cup
Savitri had to make a model of a cylindrical kalei doscope for her science probject. She wanted to use chart to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidscope of length 25 cm with a 3.5 cm radius?
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Area of chart paper required
= CSA of cylinder
A hemispherical dome of a building eneds to be painted. If circumference of base of done is 17.6 m, find cost of painting it, given cost of painting is \(\mathrm{Rs.\ 4\ per\ 100\ cm^2} \). \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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CSA
cost of painting
In a conical vessel of radius 8.4 m and vertical height 3.5 m, how many full bags of wheat can be emptied, if space for wheat in each bag is \(1.96\ m^3 \)? \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume of conical vessel
Number of bags
A solid spherical ball of diameter 4.2 cm is completely immersed in water. How much water is displaced ?
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Volume of a solid spherical ball
If the volume of a sphere is divided by its surface area, then the result is 27. Find the radius of the sphere.
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The radius of a spherical balloon is inflated from 1.5 cm to 2.5 cm by pumping more air in it. Find the ratio of surface areas of resulting balloon to the original balloon.
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Surface area of the balloon of radius
Surface area of the balloon of radius
Ratio
Three spheres of raddi 3 cm, 4 cm and 5 cm are melted together to form a single sphere. Find the radius of new sphere.
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The curved surface area of a cylinder is \(176\ cm^2 \) and its area of the base is \(38.5\ cm^2 \). Find the volume of the cylinder. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Volume
How many cubes of side \(3\ cm \) can be cut from a wooden solid cuboid with dimensions \(12\ cm \times 12\ cm \times 9\ cm\) ?
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Volume of cuboid
Volume of cube
Number of cubes
A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
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Outer radius
outer curved surface area
A hemispherical bowl is made of 0.25 cm thickness. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Outer radius
outer curved surface area
A jokerโs cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
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CSA of joker cap
CSA of joker’s cap
A metallic sheet is of the rectangular shape with dimensions \(48\ cm \times 36\ cm\). From each one of its corners a square of side \(8\ cm\) is cut off. An open box is made of the remaining sheet. Find the volume of the box.
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Length of the box
Breadth of the box
Height of the box
Volume
How many litres of water flow out through a pipe having an area of crossโsection of \(5\ cm^2\) in one minute, if the speed of water in pipe is \(30\ cm/ \sec\)?
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Speed of the water = area of cross section
If slant height of a cone is 21 m and diamter of its base is 24 m, then find its total surface area.
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TSA
Find the maximum number of cubes of sides \(3\ cm\) than can be cut out of a cubid of dimensions \(18\ cm \times 12\ cm \times 9\ cm\).
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Volume of cuboid
Volume of cube
Number of cubes
If the radius of a sphere is increased by 10%, by how much percent will its volume increase?
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Volume of sphere
Increased radius
Volume of the new sphere
Increased in volume
% increase
How many litres of water flow out of a pipe having an area of cross section of \(5\ cm^2\) in one minute, if the speed of water in the pipe is 30 cm/sec?
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Speed of the water = area of cross section
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the hemisphere, if the length of the shape be 7 cm.
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Length
Curved surface area
A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface area of the solid thus generated.
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Since the given right angled triangle is revolved about the side 8 cm, it will form a cone of radius 6 cm and height 8 cm
Volume
CSA
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down into a single cube whose diagonal is \(12\sqrt3\ cm \). Find the edge of the three cubes.
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Diagonal of the cube
Edge are 6 cm, 8 cm, 10 cm
How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m ?
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CSA
What is the least number of solid metallic spheres of 6 cm in diameter that should be melted and rescast to form a solid metal cylinder whose height is 45 cm and diameter 4 cm ?
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Volume of solid cylinder
Volume of sphere
Number of sphere