EXERCISE

If the amount of water displaced by a solid spherical ball of diameter $28 \mathrm{cm}$ is $\mathrm{V} {\mathrm{cm}}^3$, then find the value of $\mathrm{V}$ (correct to $2$ decimal places). Assume $\mathrm{\pi }=\frac{22}{7}$.

If the amount of water displaced by a solid spherical ball of diameter $0.21 \mathrm{m}$ is $\mathrm{V} {\mathrm{m}}^3$, then find the value of $\mathrm{V}$ (round off to $3$ decimal places). Assume $\mathrm{\pi }=\frac{22}{7}$.

The diameter of a metallic ball is $4.2 \mathrm{c}\mathrm{m}.$ If the density of the metal is $8.9 \mathrm{g}$ per ${\mathrm{c}\mathrm{m}}^3$, the mass of the ball is $w \mathrm{g}$, then find the value of $w$ (correct upto two decimal places). (Assume $\mathrm{\pi }=\frac{22}{7}$)

If the volume of a sphere, whose surface area is $154 \mathrm{c}{\mathrm{m}}^2$ is $\mathrm{V} {\mathrm{cm}}^3$, then find the value of $\mathrm{V}$ (correct upto two decimal places). (Assume $\mathrm{\pi }=\frac{22}{7}$).

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of $\mathrm{₹}4989.60$. If the cost of white-washing is $\mathrm{₹}20$ per square meter, and the volume of the air inside the dome is $k {\mathrm{m}}^3$, then find the value of $k$ (correct upto two decimal places). (Take $\mathrm{\pi }=\frac{22}{7}$) 

Twenty-seven solid iron spheres, each of radius $\mathrm{r}$ and surface area $\mathrm{S}$ are melted to form a sphere with surface area ${\mathrm{S}}^{\mathrm{\text{'}}}$. Find the radius $\mathrm{r}\mathrm{\text{'}}$ of the new sphere in terms of $\mathrm{r}$.

Twenty-seven solid iron spheres, each of radius $r$ and surface area $S$ are melted to form a sphere with surface area $S^{\text{'}}$. Find the ratio of $S$ and $S^{\text{'}}$.(Take $\mathrm{\pi }=\frac{22}{7}$)

A capsule of medicine is in the shape of a sphere of diameter $3.5 \mathrm{m}\mathrm{m}.$ If $A \mathrm{m}{\mathrm{m}}^3$ of medicine is needed to fill this capsule, then find the value of $A$. (Correct up to three decimal places and assume $\mathrm{\pi }=\frac{22}{7}$)