Manipur Board Solutions for Chapter: Mensuration, Exercise 4: EXERCISE 12.4

A container is formed of a hollow cylinder fitted with a hemispherical bottom of radius $3 \mathrm{cm}$. The depth of the cylinder is $14 \mathrm{cm}$ and the diameter of the hemisphere is $6 \mathrm{cm}$. Find the volume and the internal surface area of the container.

From a solid cylinder of height $28 \mathrm{cm}$ and radius $12 \mathrm{cm}$, a cone of the same height and same radius is removed. Find the volume of the remaining solid.

A cylindrical container of radius $10 \mathrm{cm}$ and height $35 \mathrm{cm}$ is fixed co-axially inside another cylindrical container of radius $14 \mathrm{cm}$ and height $35 \mathrm{cm}$. The total space between the two containers is filled with cork for insulation purposes. Find the volume of the cork required.

A solid is in the shape of a hemisphere surmounted by a cone of the same radius. The diameter of the cone is $18 \mathrm{cm}$ and the height of the cone is $14 \mathrm{cm}$. The solid is completely immersed in a cylindrical tub, full of water. If the diameter of the tub is $26 \mathrm{cm}$ and its height is $21 \mathrm{cm}$, find the quantity of water left in the cylindrical tub in litres.

A solid toy is in the form of a cone surmounted on a hemisphere of the same radius. The height of the cone is $6 \mathrm{cm}$ and the radius of the base is $2.8 \mathrm{cm}$. If a cylinder circumscribes the solid, find how much more space it will Cover.

A right triangle, with legs $9 \mathrm{cm} \text{and} 12 \mathrm{cm}$, is made to revolve about its hypotenuse. Find the volume and the surface area of the double cone so formed.

A godown is formed of a cuboid of dimensions $63 \mathrm{m}\times 28 \mathrm{m}\times 5 \mathrm{m}$ covered by a half cylindrical roof. If the length and breadth of the cuboid are $63 \mathrm{m} \text{and} 28 \mathrm{m}$ respectively, find the volume of air inside the godown. Also find the cost of roofing at the rate of $₹500 \mathrm{per} \mathrm{square} \mathrm{metre}$. 
 

A solid is in the form of a cylinder surmounted by a cone of the same radius. If the radius of the base and the height of the cone are$\mathrm{r} \mathrm{cm} \text{and} \mathrm{h} \mathrm{cm}$, respectively and the total height of the solid is $3\mathrm{h}$, prove that the volume of the solid is $\frac{7}{3}{\mathrm{\pi hr}}^2$.