EXERCISE 14.2

The largest cone is curved out from one face of solid cube of side $21 \mathrm{cm}.$ If the volume of the remaining solid is $k {\mathrm{cm}}^3$ then find $k$. (Take$\pi =22/7$)

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is $3.5 \mathrm{cm}$ and the total wood used in the making of toy is $166\frac{5}{6}$ ${\mathrm{cm}}^3.$ Find the height of the toy. Also, If the cost of painting the hemispherical part of the toy at the rate of  $₹10 \mathrm{per} {\mathrm{cm}}^2$ is $₹ k$, then write $k$. $\left(\text{ Take }\pi =\frac{22}{7}\right)$.

In the given figure, from a cuboidal solid metallic block, of dimensions $15 \mathrm{cm}\times 10 \mathrm{cm}\times 5 \mathrm{cm}$, a cylindrical hole of diameter $7 \mathrm{cm}$ is drilled out. If the surface area of the remaining block is $k {\mathrm{cm}}^2$ then find $k$. $(\mathrm{Take} \mathrm{\pi }=22/7).$

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21} {\mathrm{m}}^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building? $(\text{Use} \mathrm{\pi }=22/7)$

A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins, respectively. The dimensions of the cuboid are $10 \mathrm{cm} \times 5 \mathrm{cm}\times 4 \mathrm{cm}$.  The radius of each of the conical depression is $0.5 \mathrm{cm}$ and the depth is $2.1 \mathrm{cm}$. The edge of the cubical depression is $3 \mathrm{cm}$. If the volume of the wood in the entire stand is $k {\mathrm{cm}}^3$, then find the value of $k$. $\left(\text{Take} \mathrm{\pi }=3.14\right)$

A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to $\frac{2}{3}$ of the total height of the building. Find the height of the building, if it contains $67\frac{1}{21} {\mathrm{m}}^3$ of air. $(\mathrm{Take} \mathrm{\pi } = 22/7)$

A solid toys in the form of a hemisphere surrounded by a right circular cone. The height of cone is $4 \mathrm{cm}$ and the diameter of the base is $8 \mathrm{cm}$. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. If the total surface area of the toy rounded off to two decimal places is $k {\mathrm{cm}}^2$ then find $k$..$(\text{Use} \mathrm{\pi }=22/7)$

A circus tent is in the shape of cylinder surmounted by a conical top of same diameter. If their common diameter is $56 \mathrm{m}$, the height of the cylindrical part is $6 \mathrm{m}$ and the total height of the tent above the ground is $27 \mathrm{m}$, If the area of the canvas used in making the tent is $k {\mathrm{m}}^2$ then find $k$. $(\text{Use} \mathrm{\pi }=22/7)$