J P Mohindru and Bharat Mohindru Solutions for Chapter: Surface Areas and Volumes, Exercise 1: EXERCISE

A hemispherical depression is cut out from one face of a cubical wooden block of edge $21 \mathrm{cm}$, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and surface area of the remaining block.

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is $21 \mathrm{cm}$ and its volume is $\frac{2}{3}$ of the volume of the hemisphere, calculate the height of the cone and surface area of the toy. (Use $\mathrm{\pi }=\frac{22}{7}$ )

From a solid cylinder of height  $2.8 \mathrm{cm}$ and diameter $4.2 \mathrm{cm}$, a conical cavity of same height and same diameter is hollowed out. If the total surface area of the remaining solid is $k {\mathrm{cm}}^2$, then find the value of $k$. ( Use $\pi =\frac{22}{7}$ )

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 the value of $k$. (Use $\pi =\frac{22}{7}$ )

A metallic cylinder has radius $3 \mathrm{cm}$ and height $5 \mathrm{cm}$. To reduce its weight a conical hole is drilled in the cylinder. The conical hole has a radius of $\frac{3}{2} \mathrm{cm}$ and its depth is $\frac{8}{9} \mathrm{cm}$. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape. ( Use $\pi =\frac{22}{7}$ )

A spherical glass vessel has a cylindrical neck $7 \mathrm{cm}$ long and $4 \mathrm{cm}$ in diameter. The diameter of the spherical part is $21 \mathrm{cm}$. If the quantity of water it can hold is $k {\mathrm{cm}}^3$, then find the value of $k$. (Take $\mathrm{\pi }=\frac{22}{7}$)

From a cubical piece of wood of side $21 \mathrm{cm}$, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece. (Take $\pi =\frac{22}{7}$)

A cubical block of side $10 \mathrm{cm}$ is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of $₹5$ per $100 \mathrm{sq}.\mathrm{cm}$. (Use $\mathrm{\pi }=3.14$)