Question

A tent in the shape of a right circular cylinder up to a height of 3m and conical above it. The total height of the tent is 13.5m and the radius of its base is 14m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre

Answer 1

CSA of cylinder =2πrh
$2 \times \frac{22}{7} \times 14 \times 3 \\ = 264 {m}^{2}$

radius=14m
height =13.5-3=10.5

$l {}^{2} = r {}^{2} + h {}^{2}$
$14 { }^{2} + 10.5 { }^{2} \\ 196 + 110.25 \\ = 306.25 \\ l \sqrt{306.25 } \\ l = 17.5m$

CSA of cone =πrl

$\frac{22}{7} \times 14 \times 17.5 \\ = 770 {m}^{2}$
total area=264+770
$1034 {m}^{2}$
cost of cloth per square m = Rs80
cost of cloth
$1034 {m}^{2}$
$80 \times 1034 \\ = 82720$

Answer 2

r=14,h of cylinder=3, h of Cone=10.5
S.A.of cylinder=2×22/7×14×3=264
slant height=√10.5²+14²=17.5
C.S.A of cone =22/7×14×17.5=770
T.S.A. of tent =770+264=1034m²
cost=1034×80=82720m²