Ram Chandra Solutions for Chapter: Mensuration, Exercise 2: Enrichment Exercise

Edge of a cube is $l.$ Its volume is $l^3$.

If dimensions of a cuboid are $2a$, $3b$ and $4c$, then its total surface area is $24abc$square units.

If $‘r’$ is the base radius and $\text{'}l\text{'}$ be the slant height. Then the volume of the cone is $\frac{1}{3}\pi r^{3}l$.

The radius of a sphere is reduced to $\frac{1}{3}r$.  The total surface area of the new sphere will be $\frac{4}{3}\pi r^2 \mathrm{sq}. \mathrm{units}.$

If length of cuboid is doubled, keeping its breadth and height same then the total surface area of the new cuboid is $2[2lb+\mathrm{bh}+2hl] \mathrm{sq}. \mathrm{units}.$

The edge of a cube is $‘r’ \mathrm{cm}$. Volume of the possible largest circular cone that can be cut-out of this cube is $\frac{1}{6}\pi r^3 {\mathrm{cm}}^3$.

If the radius of a right circular cone is halved and height is doubled then its volume remains unchanged.

A largest sphere is carved from a cube of edge $‘r’$. The volume of the sphere so obtained is $\frac{\pi r^3}{6} \mathrm{cu}. \mathrm{units}$.