The diagram shows a frustum. It was made by standing a cone on its base and slicing a smaller cone off the top, parallel to the base.

The frustum has base radius \(15\) cm, top radius \(3\) cm and height \(32\) cm.

Find the height of the cone that was removed.

A cone of height \(54\) cm and base radius \(18\) cm had a smaller cone sliced off the top, parallel to the base. The solid left behind is the frustum shown.

The top of the frustum is a circle of radius \(3\) cm, and the cone that was removed is \(9\) cm tall.

Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

Work out the volume of the frustum. Give your answer in terms of \(\pi\).

A solid cone has base radius \(15\) cm and height \(45\) cm.

A cone of height \(18\) cm is removed from the top of it, by cutting parallel to the base. The solid left behind is the frustum shown.

Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

Here is a frustum, made by slicing a smaller cone off the top of a cone of slant height \(60\) cm.

The base radius is \(20\) cm and the top radius is \(5\) cm.

Curved surface area of a cone \(= \pi r l\), where \(l\) is the slant height.

Work out the curved surface area of the frustum. Give your answer in terms of \(\pi\).

A vase is the shape of a frustum, made by removing a cone of height \(36\) cm from the top of a cone of height \(60\) cm. It stands on its wider end, and the opening is the smaller circle on top.

The base has radius \(10\) cm, the opening has radius \(6\) cm, and the vase is \(24\) cm deep.

Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

Work out how many litres of water the vase holds when full. Give your answer to 1 decimal place.

\(1\) litre \(= 1000\) cm³

A light shade is made from card stretched around the curved surface of a frustum. It is open at both ends.

The frustum was cut from a cone of slant height \(54\) cm. Its two circular ends have radii \(18\) cm and \(6\) cm.

Curved surface area of a cone \(= \pi r l\), where \(l\) is the slant height.

Find the area of card needed. Give your answer to 1 decimal place.

The diagram shows a frustum. It was made by standing a cone on its base and slicing a smaller cone off the top, parallel to the base.

The frustum has base radius \(12\) cm, top radius \(4\) cm and height \(20\) cm.

Calculate the height of the cone that was removed.

A cone of height \(36\) cm and base radius \(6\) cm had a smaller cone sliced off the top, parallel to the base. The solid left behind is the frustum shown.

The top of the frustum is a circle of radius \(4\) cm, and the cone that was removed is \(24\) cm tall.

Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

Calculate the volume of the frustum. Give your answer in terms of \(\pi\).

A solid cone has base radius \(18\) cm and height \(54\) cm.

A cone of height \(24\) cm is removed from the top of it, by cutting parallel to the base. The solid left behind is the frustum shown.

Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

Here is a frustum, made by slicing a smaller cone off the top of a cone of slant height \(60\) cm.

The base radius is \(20\) cm and the top radius is \(8\) cm.

Curved surface area of a cone \(= \pi r l\), where \(l\) is the slant height.

Calculate the curved surface area of the frustum. Give your answer in terms of \(\pi\).