Surface Areas a...

A container made up of metal sheet is in the form of a frustum cone of height $$20$$ cm with radii of its lower and upper ends $$4$$ cm and $$16$$ cm respectively. The amount of liquid the container can hold is (Use $$\pi = 3$$)

The radii of the ends of a frustum of a cone are $$28\ cm$$ and $$7\ cm$$. The height of the cone is $$40\ cm$$, find its volume.

Calculate the volume of a frustum cone given above:

The height of the frustum cone is $$24$$ ft. The area of the top and bottom circle of the cone is $$6 ft^2$$ and $$10 ft^2$$ respectively. Find its volume.

A bucket of height $$16\ cm$$ made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as $$3\ cm$$ and $$15\ cm$$ respectively. What is the slant height of the bucket?

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is $$10$$ cm, and its base is of radius $$3.5$$ cm, find the volume of wood in the toy. $$\displaystyle \left[ Use \,\,\, \pi = \frac{22}{7} \right]$$

Adithi has a set of identical cubes. She makes solids by gluing together $$4$$ of these cubes. When cube faces are glued together, they must coincide. Each of the $$4$$ cubes must have a face that coincides with a face of at least one of the other $$3$$ cubes. One such solid is shown. Find the number of unique solids that Adithi can make using the $$4$$ cubes.

The solid brick shown is made of small bricks of side $$1$$. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surface area of the large brick?

A bucket which is in the form of a frustum of a cone, has radii $$3$$ and $$5$$ units and vertical height $$6$$ units. How much water can the bucket hold?

A sphere and a cube have same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube?