H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Surface Areas & Volumes, Exercise 5: EXERCISE

The radii of the ends of a bucket, $30 \mathrm{cm}$ high are $21 \mathrm{cm}$ and $7 \mathrm{cm}$. Determine, the area of the sheet required to make this bucket.

A metallic right circular cone $20 \mathrm{cm}$ high and whose vertical angle is ${90}^{\circ }$ is cut into two parts at the middle point of its height by a plane parallel to the base. If the frustum so obtained be drawn into a wire of diameter $1/16 \mathrm{cm}$, find the length of the wire.

An oil funnel of tin sheet consists of a cylindrical portion $8 \mathrm{cm}$ long attached to a frustum of a cone. If the total height be $11 \mathrm{cm}$, the diameter of the cylindrical portion $2 \mathrm{cm}$ and the diameter of the top of the funnel $14 \mathrm{cm}$, find the area of the tin required.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be $13 \mathrm{metres}$ and $7 \mathrm{metres}$, the height of the frustum $8 \mathrm{metres}$ and the slant height of the conical cap $12 \mathrm{metres}$, find the number of $\mathrm{square} \mathrm{metres}$ of canvas required for the tent.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be $16 \mathrm{metres}$ and $10 \mathrm{metres}$, the height of the frustum $8 \mathrm{metres}$ and the slant height of the conical cap $12 \mathrm{metres}$, find the number of $\mathrm{square} \mathrm{metres}$ of canvas required for the tent.

Hanumappa and his wife Gangavva are busy making jaggery out of sugarcane. They have processed the sugarcane juice to make the molasses which is poured into moulds. It will be cooled to solidify in this shape to be sent to the market. Each mould is in the shape of a frustum of a cone having the radii of its two circular faces as $30 \mathrm{cm}$ and $35 \mathrm{cm}$ and the height of the mould is $14 \mathrm{cm}$. If each ${\mathrm{cm}}^3$ of molasses weighs about $1.2 \mathrm{gm}$, find the weight of molasses that can be poured into each mould.

A shuttlecock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere. The external diameter of the frustum are $5 \mathrm{cm}$ and $2 \mathrm{cm}$, the height of the entire shuttlecock is $7 \mathrm{cm}$. Find its external surface area.

A pedestal is constructed in the form of the frustum of a pyramid, the sides of the square ends of the frustum being $360 \mathrm{cm}.$ and $160 \mathrm{cm}$ and its slant height $260 \mathrm{cm}$. Find volume, lateral surface area including area of the top and the cost of construction $@₹50$ per $\mathrm{cubic} \mathrm{metre}$ and Plastering it $@₹10$ per $\mathrm{square} \mathrm{metre}$.