Chhattisgarh Board Solutions for Exercise 8: Exercise – 4

By melting down a sphere of radius $10.5 \mathrm{cm}$ somes mall cones are made, each of height $3 \mathrm{cm}$ and radius $3.5 \mathrm{cm}$. Find the number of such cones.

After filling the air in a spherical balloon of radius $7 \mathrm{cm}$ it becomes $14 \mathrm{cm}$. Calculate the ratio of the surface area of the balloon in both conditions.

Calculate the volume of a sphere having surface area equal to $154 {\mathrm{cm}}^2$. (Use $\mathrm{\pi }=\frac{22}{7}$)

Ratio of the volume of $2$ spheres is $64:27$. Calculate the ratio of their surface areas.

Radius of a solid sphere is $12 \mathrm{cm}$. How many spheres of radius $6 \mathrm{cm}$ can be made by melting this sphere.

If the volume and surface area of a sphere are equal then calculate its radius.

A child converts a cone of height $24 \mathrm{cm}$ and base radius $6 \mathrm{cm}$ into a sphere. Calculate the radius of the sphere in $\mathrm{cm}$.

By melting down $3$ spherical balls of radius $6 \mathrm{cm}, 8 \mathrm{cm}$ and $10 \mathrm{cm}$ one big solid sphere is made. Calculate the radius (in $\mathrm{cm}$) of the new solid sphere.