Curved Surface Area of a Cone = $πrl$
where $r$ = radius of the right circular cone
$l$ = slant height of right circular cone.
Also, Note that $l^2$ = $r^2$ + $h^2$
where $h$ is the height of the cone.
Now if the base of the cone is to be closed, then a circular piece of paper of radius $r$
is also required whose area is $πr^2$.
Total Surface Area of a Cone = Curved Surface Area of a Cone + area of base of cone
= $πrl$ + $πr^2$
1. Diameter of the base of a cone is 10.5 $cm$ and its slant height is 10 $cm$. Find its curved surface area.
2. Find the total surface area of a cone, if its slant height is 21 $m$ and diameter of its base is 24 $m$.
3. Curved surface area of a cone is 308 $cm^2$ and its slant height is 14 $cm$. Find
(i) radius of the base and
(ii) total surface area of the cone.
4. A conical tent is 10 $m$ high and the radius of its base is 24 $m$. Find
(i) slant height of the tent.
(ii) cost of the canvas required to make the tent, if the cost of 1 $m^2$ canvas is ₹ 70.
5. What length of tarpaulin 3 $m$ wide will be required to make conical tent of height 8 $m$ and base radius 6 $m$? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 $cm$ (Use π = 3.14).
6. The slant height and base diameter of a conical tomb are 25 $m$ and 14 $m$ respectively. Find the cost of white-washing its curved surface at the rate of ₹ 210 per 100 $m^2$.
7. A joker’s cap is in the form of a right circular cone of base radius 7 $cm$ and height 24 $cm$. Find the area of the sheet required to make 10 such caps.
8. 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 $cm$ and height 1 $m$. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per $m^2$, what will be the cost of painting all these cones? (Use π = 3.14 and take √1.04 = 1.02)