Exercise

The curved surface area of a cone is $4070 {\mathrm{cm}}^2$and its diameter is $70 \mathrm{cm}$. What is its slant height?

Surface area of a sphere and cube are equal. Then find the ratio of their volumes.

Two cubes each of volume $64 {\mathrm{cm}}^3$ are joined end to end together. Find the total surface area of the resulting cuboid. 

The upper portion of the greenhouse shown in figure is semicircular. This greenhouse is made up of cloth. It has a wooden door of size $1.2 \mathrm{m}\times 0.5 \mathrm{m}$. Find the area of the cloth required to cover the greenhouse completely.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is $10 \mathrm{c}\mathrm{m}$, and its base is of radius $3.5 \mathrm{c}\mathrm{m}$, find the total surface area of the article.

A spherical glass vessel has a cylindrical neck $8 \mathrm{c}\mathrm{m}$ long, $2 \mathrm{c}\mathrm{m}$ in diameter; the diameter of the spherical part is $8.5 \mathrm{c}\mathrm{m}$. Find the amount of water it holds (taking the above as the inside measurements and $\mathrm{\pi }=3.14$).

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1 \mathrm{c}\mathrm{m}$ and the height of the cone is equal to its radius. Find the volume of the solid.

A welcome drink is served to the $100$ guests at a party. Each guest will get an equal portion of the drink in a cup as shown below.

According to the given measurement, the minimum quantity of the welcome drink required to serve all the guests once is _____ litres.