Goa Board Solutions for Chapter: Surface Areas and Volumes, Exercise 3: EXERCISE

Take, $\mathrm{\pi }=\frac{22}{7}$. 
The curved surface area of a cone is $308 \mathrm{c}{\mathrm{m}}^2$ and its slant height is $14 \mathrm{c}\mathrm{m}.$ If the radius of the base is $k \mathrm{cm}$, find $k$.

Curved surface area of a cone is $308 \mathrm{c}{\mathrm{m}}^2$ and its slant height is $14 \mathrm{c}\mathrm{m}.$ If the total surface area of the cone is $k {\mathrm{cm}}^2$, find $k$. $\left(\mathrm{Use} \pi =\frac{22}{7}\right)$

A conical tent is $10 \mathrm{m}$ high and the radius of its base is $24 \mathrm{m}.$ If the slant height of the tent is $k \mathrm{m}$, find $k$.

A conical tent is $10 \mathrm{m}$ high and the radius of its base is $24 \mathrm{m}$. Find the cost of the canvas required to make the tent, if the cost of $1 {\mathrm{m}}^2$ canvas is $\mathrm{₹} 70$. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

If the length of tarpaulin $3 \mathrm{m}$ wide will be required to make conical tent of height $8 \mathrm{m}$ and base radius $6 \mathrm{m}$ is in the form of $k \mathrm{m}$, find the value of $k$. Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20 \mathrm{c}\mathrm{m}.$ (Use $\mathrm{\pi }=3.14$).

The slant height and base diameter of a conical tomb are $25 \mathrm{m}$ and $14 \mathrm{m}$ respectively. Find the cost of whitewashing its curved surface at the rate of $\mathrm{₹}210$ per $100 {\mathrm{m}}^2$. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

A joker’s cap is in the form of a right circular cone of base radius $7 \mathrm{c}\mathrm{m}$ and height $24 \mathrm{c}\mathrm{m}.$ If the area of the sheet required to make $10$ such caps is $k {\mathrm{cm}}^2$, find $k$. $\left(\mathrm{Use} \mathrm{\pi }=\frac{22}{7}\right)$

A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled cardboard. Each cone has a base diameter of $40 \mathrm{c}\mathrm{m}$ and height $1 \mathrm{m}.$ If the outer side of each of the cones is to be painted and the cost of painting is $\mathrm{₹}\mathrm{}12$ per ${\mathrm{m}}^2.$ If the cost of painting all these cones is expressed in the form of $₹k$, find the value of $k$ up to three decimal places. (Use $\mathrm{\pi }=3.14$ and take $\sqrt{1.04}=1.02$).