Question Bank
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The volume of a hemisphere is 18π cm³. Find its radius.
What is the volume of a pyramid with a rectangular base of 10 cm by 6 cm and height 5 cm?
A cube has a total surface area of 96 cm². What is its volume?
The capacity of a cylindrical vessel is 15.4 liters. If its height is 10 cm, find the base area in cm².
Find the volume of a sphere whose surface area is 154 cm².
If the volume of a cuboid is 3000 cm³ and its base area is 150 cm², what is its height?
A sphere is inscribed in a cube of side 10 cm. What is the volume of the sphere?
Three metal cubes of sides 3 cm, 4 cm, and 5 cm are melted to form a single cube. Find the side of the new cube.
A cylindrical tank of radius 7 m and height 10 m is full of water. If this water is poured into a rectangular tank of length 22 m and width 10 m, what will be the height of water?
Find the volume of a hollow cylinder with external radius 5 cm, internal radius 4 cm, and height 10 cm.
If the radius of a cylinder is doubled and the height is halved, what is the ratio of the new volume to the original volume?
A solid cone of height 24 cm and radius of base 6 cm is melted and reshaped into a sphere. Find the radius of the sphere.
The sum of length, breadth, and height of a cuboid is 19 cm and its diagonal is 11 cm. Find its volume if the surface area is not needed but related? (Wait, let's use a standard volume problem). A cuboid has dimensions in the ratio 3:2:1 and volume 1296 cm³. Find the length.
A hemisphere and a cone have equal bases. If their heights are also equal (height of hemisphere being its radius), find the ratio of their volumes.
The volume of two spheres are in the ratio 64:27. Find the ratio of their surface areas.
A well of diameter 2 m is dug 14 m deep. The earth taken out is spread evenly to form a platform 5 m by 2 m. Find the height of the platform.
A right circular cone is 3.6 cm high and its base radius is 1.6 cm. It is melted and recast into a right circular cone with base radius 1.2 cm. Find its height.
How many bullets can be made out of a lead cylinder 28 cm high and 6 cm radius, each bullet being 1.5 cm in diameter?
The base of a right pyramid is a square of side 10 cm. If its volume is 400 cm³, find its total height.
A metal pipe has an external diameter of 4 cm and internal diameter of 3 cm. If its length is 20 cm, find the volume of metal used.