# Surface Area

## Exercise 13.3

### Part 2

Question 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).

**Answer:** h = 8 m, r = 6 m

Here: `l^2=h^2+r^2`

`=8^2+6^2``=64+36=100`

Or, `l=sqrt(100)=10` m

Curved Surface Area of cone `=π\rl`

`=3.14xx6xx10=188.4` sq m

Hence, required length of material `=(188.4)/3+0.2``=62.8+0.2=63` m

Question 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 Rs 210 per 100 m^{2}.

**Answer:** l = 25 m, d = 14 m or, r = 7 m

CSA of cone `=π\rl`

`=(22)/7xx7xx25=550` sq m

Cost = Area × Rate

`=550xx(210)/(100)` = Rs. 1155

Question 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.

**Answer:** r = 7 cm, h = 2 cm

Here: `l^2=h^2+r^2`

`=24^2+7^2``=576+49=625`

Or, `l=sqrt(625)=25` cm`

CSA `=π\rl`

`=(22)/7xx7xx25=550` sq cm

Area of sheet for 10 caps `=550xx10=5500` sq cm

Question 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 Rs 12 per m^{2}, what will be the cost of painting all these cones? (Use π = 3.14 and take ∠1.04 = 1.02)

**Answer:** d = 40 cm or, r = 20 cm, h = 1 m

Here: `l^2=h^2+r^2`

`=1^2+(0.2)^2``=1+0.04=1.04`

Or, `l=sqrt(1.04)=1.02`

CSA of cone `=π\rl`

`=3.14xx1.02xx0.2`

CSA of 50 cones `=3.14xx1.02xx0.2xx 50`

`=3.14xx1.02xx10=32.028`

Cost = Area × Rate

`=32.028xx12` = Rs. 384.33