a tent is in the shape of a cylinder surmounted by a cone, the diameter of cylindrical part is 16m - Maths - Surface Areas and Volumes

Question

a tent is in the shape of a cylinder surmounted by a cone, the
diameter of cylindrical part is 16m and height is 10m if the vertex
of the tent is 16m above the ground , find the area of canvas
required to make the tent

Priyanka Kedia · Accepted Answer

$G i v e n t h a t, t h e d i a m e t e r o f c y l i n d r i c a l p a r t = 16 c m S o, r a d i u s o f c y l i n d r i c a l p a r t = \frac{16}{2} = 8 c m A n d, h e i g h t o f c y l i n d r i c a l p a r t = 10 m C u r v e d s u r f a c e a r e a o f c y l i n d e r = 2 π r h = 2 π \times 8 \times 10 = 160 π N o w, c y l i n d e r i s s u r m o u n t e d b y a c o n e . S o, r a d i u s o f c o n e = r a d i u s o f c y l i n d e r = 8 c m H e i g h t o f c o n e = t o t a l h e i g h t - h e i g h t o f c y l i n d e r = 16 - 10 = 6 m S l a n t h e i g h t o f c o n e (l) = \sqrt{r^{2} + h^{2}} = \sqrt{{(8)}^{2} + {(6)}^{2}} = \sqrt{64 + 36} = 10 m T h u s, C u r v e d s u r f a c e a r e a o f c o n e = π r l = π \times 8 \times 10 = 80 π A r e a o f c a n v a s r e q u i r e d t o m a k e t h e t e n t = C . S . A . o f c y l i n e r + C . S . A . o f c o n e = 160 π + 80 π = 240 π m^{2} H e n c e, A r e a o f c a n v a s r e q u i r e d t o m a k e t h e t e n t i s 240 π m^{2}$

a tent is in the shape of a cylinder surmounted by a cone, the diameter of cylindrical part is 16m and height is 10m. if the vertex of the tent is 16m above the ground , find the area of canvas required to make the tent