Goa Board Solutions for Chapter: Surface Areas and Volumes, Exercise 4: EXERCISE

The radius of a spherical balloon increases from $7 \mathrm{c}\mathrm{m}$ to $14 \mathrm{c}\mathrm{m}$ as air is being pumped into it. Find the ratio of initial surface area of a balloon to final surface area of a balloon. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

A hemispherical bowl made of brass has inner diameter $10.5 \mathrm{c}\mathrm{m}.$ If the cost of tin-plating it on the inside at the rate of $\mathrm{₹} 16$ per $100 \mathrm{c}{\mathrm{m}}^2$ is  $\mathrm{₹}k$ then find the value of $k$. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

Assume $\mathrm{\pi }=\frac{22}{7}$
A sphere's surface area is $154 \mathrm{c}{\mathrm{m}}^2$. If the radius of the sphere is $k \mathrm{cm}$, then the value of $k$ is (Write the answer in decimal form)

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of surface areas of moon to earth. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

A hemispherical bowl is made of steel, $0.25 \mathrm{c}\mathrm{m}$ thick. The inner radius of the bowl is $5 \mathrm{c}\mathrm{m}.$ If the outer curved surface area of the bowl is $k {\mathrm{cm}}^2$, then find $k$. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

A right circular cylinder just encloses a sphere of radius $r$. The surface area of the sphere is $K{\mathrm{\pi r}}^2$. Find $K$.

Assume $\mathrm{\pi }=\frac{22}{7}$.
A right circular cylinder just encloses a sphere of radius $\mathrm{r}$.

If the curved surface area of the cylinder is of the form $k\times {\mathrm{\pi r}}^2$, then find the value of $k$.

A right circular cylinder just encloses a sphere of radius $\mathrm{r}$ (see figure). If the ratio of surface area of the sphere and curved surface area of the cylinder is $1:k,$ then find the value of $k.$(Use $\mathrm{\pi }=\frac{22}{7}$)