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The volume of the frustum of a cone of height 20 in, large base radius to be 25 in, and slant height to be 29 is  π in3.

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Important Questions on Surface Areas and Volumes

EASY
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A tank is in the form of a cuboid with length 12 m. If 18 kilolitre of water is removed from  water level goes down by 30 cm. What is the width (in m ) of the tank?
EASY
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

By melting a solid cylinder of radius 3 cm and height 20 cm, five spherical balls each of same size are formed. Find the radius of each ball. 

(A) 2 cm

(B) 3 cm 

(C) 4 cm 

(D) 5 cm 

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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A spherical ball of the lead of radius 14 cm is melted and recast into spheres of radius 2 cm. The number of the small sphere is:
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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A solid hemisphere is attached to the top of a cylinder, having the same radius as that of the cylinder. If the height of the cylinder were doubled (keeping both radii fixed), the volume of the entire system would have increased by 50%. By what percentage would the volume have increased if the radii of the hemisphere and the cylinder were doubled (keeping the height fixed)?
 
HARD
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
Suppose the height of a pyramid with a square base is decreased by p% and the lengths of the sides of its square base are increased by p% (where p>0 ). If the volume remains the same, then
EASY
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to.

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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid

The length and breadth of a rectangular sheet are 48 m and 36 m respectively. A square is cut off from each of its corners, so that an open box be made. If the side of square be 16m, what will be the volume of the box so formed (in cubic m)? 

(A) 1,024 

(B) 1,224 

(C) 1,324 

(D) 1,124 

MEDIUM
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A cube of side 1 m length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
HARD
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
Given are three cylindrical buckets X,Y,Z whose circular bases are of radii 1,2,3 units, respectively. Initially water is filled in these buckets upto the same height. Some water is then transferred from Z to X so that they both have the same volume of water. Some water is then transferred between X and Y so that they both have the same volume of water. If hY,hZ denote the heights of water at this stage in the buckets Y, Z, respectively, then the ratio hYhZ equals
EASY
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the new sphere will be _____.
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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
The number of solid cones with integer radius and integer height each having its volume numerically equal to its total surface area is
EASY
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
If x4+y4=706 and  xy=15, find the value of x2+y2+2.
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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A bottle in the shape of a right-circular cone with height h contains some water. When its base is placed on a flat surface, the height of the vertex from the water level is a units. When it is kept upside down, the height of the base from the water level is a4 units. Then the ratio ha is
EASY
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into x toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of x is:
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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such spheres can be made?
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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is 243 cm. The volume (in cm3) of the pyramid is:
MEDIUM
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
The radius and the height of a right circular cone are in the ratio 5:12. Its curved surface area is 816.4 cm2. What is the volume (in cm3) of the cone? (take π=3.14)
MEDIUM
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
A spherical ball of a lead of the radius 14 cm is melted and recast into spheres of the radius 2 cm.The number of small spheres is:
HARD
Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
On each face of a cuboid, the sum of its perimeter and its area is written. Among the six numbers so written, there are three distinct numbers and they are 16, 24 and 31. The volume of the cuboid lies between
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Mathematics>Geometry>Surface Areas and Volumes>Frustum of a Pyramid
The slant height of the frustum of a cone is 4 cm and the perimeter of its circular bases are 18 cm and 6 cm respectively. Find the curved surface area of the frustum.