A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 - Maths - Surface Areas and Volumes

Question

A cloth having an area of 165 m2 is shaped into the form of a
conical tent of radius
5 m
(i) How many students can sit in the tent if a student, on an
average, occupies
5 2
7
m on the ground?
(ii) Find the volume of the cone

Priyanka Kedia · Accepted Answer

Given, A cloth having an area of 165 $m^{2}$ is shaped into the form of a conical tent of radius 5 m.

So, Radius of conical tent (r) = 5 m

And, l and h be the Slant height and height of the cone respectively.

Now, area occupied by one student = 5/7 $m^{2}$

So,

$N o . o f s t u d e n t = \frac{A r e a o f c i r c u l a r b a s e o f t h e c o n e}{A r e a o c c u p i e d b y o n e s t u de n t} = \frac{π r^{2}}{5 / 7} = \frac{\frac{22}{7} \times 5^{2}}{5 / 7} = 22 \times 5 = 110$

Also,

$C u r v e d s u r f a c e a r e a o f c o n e = π r l \Rightarrow 165 = \frac{22}{7} \times 5 \times l \Rightarrow l = 10.5 m A n d, h = \sqrt{l^{2} - r^{2}} = \sqrt{{(10.5)}^{2} - 5^{2}} = \sqrt{110.25 - 25} = \sqrt{85.25} = 9.233 m \Rightarrow h = 9.23 m T h u s, V o l u m e o f t h e c o n e = \frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times 5^{2} \times 9.23 = 241.738 m^{2}$

Hence, 110 students can sit in the tent and volume of cone is 241.738 $m^{2}$ .

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m (i) How many students can sit in the tent if a student, on an average, occupies 5 2 7 m on the ground? (ii) Find the volume of the cone.

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius

5 m

(i) How many students can sit in the tent if a student, on an average, occupies

5 2

7

m on the ground?

(ii) Find the volume of the cone.