CHAPTER TEST

The largest possible cube is made from a wooden sphere of radius $6\sqrt{3} \mathrm{cm}$. Find the surface area of the cube. (Write the answer without unit)

Out of a solid cube of side $28 \mathrm{cm}$ the largest possible sphere is carved out. Find the Volume of the sphere to the first place of decimal.

A sphere of diameter $6 \mathrm{cm}$ is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is $12 \mathrm{cm}$ . If the sphere is completely submerged in water, find the rise of the  water level in the cylindrical vessel.

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the base of a cylinder and the cone is $24 \mathrm{m}$. The height of the cylinder is $11 \mathrm{m}$. If the vertex of the cone is $16 \mathrm{m}$ above the ground, find the area of the canvas required for making the tent. (Write the answser without unit)

A rectangle reservoir is $120 \mathrm{m}$ long and $75 \mathrm{m}$ wide. At what speed per hour must water flow into it through a square pipe of $20 \mathrm{cm}$ side so that the water rises by $2.4 \mathrm{m}$ in $18$ hours?

A well of diameter $3 \mathrm{m}$ is dug $14 \mathrm{m}$ deep. The earth taken out of it is spread evenly all round it in the shape of a circular ring of width $4 \mathrm{m}$ to form an embankment. Find the height of the embankment. 

A bucket is in the frustum of a cone and hold $28.49$ litres of milk. The radii of the top and bottom are $28 \mathrm{cm}$ and $21 \mathrm{cm}$ respectively. Find the height of the bucket.

A vessel is in the form of an inverted cone. Its height is $11 \mathrm{cm}$ and the radius of its top which is open is $2.5 \mathrm{cm}$. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius $0.25 \mathrm{cm}$ are dropped into the vessel , $\frac{2}{5}$ of water flows out. FInd the number of lead shots dropped into the vessel.