Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Surface Areas and Volumes, Exercise 4: Challengers*

A hemispherical bowl is $176 \mathrm{cm}$ and round the brim. Supposing it to be half-filled, then how many persons may be served frotn it in hemi-spherical glasses $4 \mathrm{cm}$ in diameter at the top?

The sum of the radii of two spheres is $10 \mathrm{cm}$ and the sum of their volumes is $880 {\mathrm{cm}}^3$. Then what will be the product of their radil?

A child consumed an ice-cream of inverted right circular conical shape from the top and left only $12.5\%$ of the cone for her mother. If the height of the ice-cream cone was $8 \mathrm{cm}$, then what was the height of the remaining ice-cream cone?

The radius and height of a right solid circular cone $\left(ABC\right)$ are respectively $6 \mathrm{cm}$ and $2\sqrt{7} \mathrm{cm}$. A coaxial cone $\left(DEF\right)$ of radius $3 \mathrm{cm}$ and height $\sqrt{7} \mathrm{cm}$ is cut out of the cone as shown in the given figure. Then what is the whole surface area of the solid thus fotmed?