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The area of three adjacent faces of a cuboid are \(x,y,z\) if the volume is \(V \), then \( V^2\) will be equal to
The volume of a sphere of diameter 2p cm is given by
Diameter
Radius
Volume
The maximum length of pencil which can be put inside the box whose dimensions are 8cm, 6cm, 2cm
Max. length
One room’s breadth is double its height and half its length. If volume of room is \(512\ m^3 \) then length of the room will be
Let the breadth be
Volume
A rectangular wooden block whose dimensions are 15cm long, 12cm wide and 6 cm high. How many minimum cubes to be made by its block.
Volume
volume of one cube
So, 40 minimum cube can be made
Diameter of a cylinder vessel is 60cm. it is filled with water such that a sphere of diameter 30cm is mersed fully into it. Then what is the increase in height of the water surface after putting the sphere in the vessels.
Volume of the sphere
Volume of cylinder
A village having a population of 4000 requires 150 liter per head per day. It has a tank measuring 20 m by 15m by 6m. for how many days the water of this tank will last.
Total requirement of water in a day
No. of days
A drum of water is \(\dfrac{3}{5} \) full. When 57 liters are drawn from it, it is just \(\dfrac{1}{8} \) full. Find the total capacity of drum.
Let the total capacity of drum be
If the length, breadth and height of a cube are increased, decreased and increased by 1%, 3%, 2% respectively then the volume of solid.
Volume
New volume
So, the volume will decrease
Solids of various shapes are cost from equal volumes of metal. The least surface will be possessed by
The least surface will be possessed by the cylinder
A wire in the shape of an equilateral triangle has an area S sq cm. If the same wire is bent to form a circle, the area of the circle will be
sq cm
Perimeter of triangle = perimeter of circle.
Area of circle
Solving we get
A wire of length 2p is bent to form a circle, a triangle, a rectangle and a polygon. State which figure he greatest area.
Rectangle has greatest area
A right circular cylinder, a right circular cone and a hemisphere are all having equal base area and height. These volumes are in the ratio.
A rectangular sheet of cardboard is 9cm by 6cm. If greatest possible circle is cut off from cardboard, the remaining area is
Area of circle
Area of cardboard
Remaining area
A cone is cut half way through its axis and parallel to the base the volume of two portions are in the ratio.
Volume of frustum,
Three cubes of metal of edges 6cm, 8cm and 10cm are melted to form a new cube. Find the diagonal of this cube
Let the edge of new cube be
Diagonal of new cube
The dimension of a brick are 24 cm × 12 cm × 8 cm. How many bricks will be required to build a wall 24m × 8m × 6m if 20% of the wall is filled with mortar?
Volume of brick
Volume of wall
Volume left
Number of bricks
The area of 4 walls of the hall whose breadth is 15m and height is 8m is 1068 sqm, the length of the hall is
Area of walls
The perimeter of the following shaded portion is
length of arc LE = arc FG = arc HI = arc JK
Perimeter of the shaded portion
The area of the shaded region is
unit
Area of the shaded region
sq unit
The internal and external diameters of a hollow hemispherical vessel are 42 cm and 45.5 cm respectively. Find the capacity
capacity
capacity
The volume of a versal in the form of a right circular cylinder is \(448\pi\ cm^3 \) and height is \( 7\ cm\). Find the radius
A cubical block of side 7 cm is sumounted by a hemisphere. What is the greatest diameter the hemisphere can have?
Diameter is equal to the cube’s edge ie 7 cm
\(2 \) cubes each of volume \(64\ cm^3 \) are joined end to end. Find the surface area of the resulting cuboids.
Edge
Surface area of cuboid
A cuboidal metal of dimensions \(44\ cm \times 30\ cm \times 15\ cm\) was melted and cast into a cylinder of height \(28\ cm\). find its radius
Volume of cuboid = volume of cylinder
The L.S.A of a cylinder is \(176\ cm^2 \) and base area is \(38.5\ cm^2 \). What is its volume?
The side of a solid metallic cube is 50 cm. It is melted and recast into 8000 similar solid cubical dice. Find the side of each die
Volume
Let cm be the side of a cubical dice volume of dice
A/Q
A cylindrical vessel contains 49.896 liters of liquid. The cost of painting its C.S.A at 2 paise/sq cm is ‘ 95.04. Find its total surface area.
A right angled triangle \(ABC \), where \(\angle B=90^o \) is rotated about \(BC \). If \(BC=16\ cm \) and \(AC=20\ cm \). Find the volume of the right circular cone.
A cylindrical can whose base is horizontal and of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed in the can, water just covers the sphere. Find the depth of water in the can before the sphere was put into it.
Let the initial depth of water be cm.
Volume
volume of the sphere
A/Q