Question

Swasti has a piece of canvas whose area is 551m square. she uses it to make a conical tent with a base radius of 7 cm. assuming that all the stiching margins and wastage incurred while cutting amounts to approximately 1m square ,find the volume of the tent that can be made with it.

Answer 1

Clearly, the lateral/curved surface area of the cone =(Total area of the canvas) - (Area of canvas wasted).
=551 sq m - 1 sq m
=550 sq m
Now, let the slant height be l m.
Therefore, curved surface area =πrl
=(22/7)(7)l
Thus,
(22/7)(7)l = 550
=> l = (550×7)/(22×7)
=> l = 25
We have; height=√(l^2 - r^2)
=√(25^2-7^2) m
=√{(25+7)×(25-7)} m
=√(576) m
=24 m
Therefore, volume of the cone =(1/3)π(r^2)h
=(1/3)×(22/7)×(7×7)×24 sq m.
=1232 sq m. [Answer]
Hope this helps. While solving any problem, make an appropriate diagram to make your solution more clear and visualize it in your mind. If there is any problem in the units of measurement used in this solution, please replace it with the correct unit by making changes accordingly. Please comment for further clarification if needed. Thanks!

Answer 2

Answer:

Clearly, the lateral/curved surface area of the cone =(Total area of the canvas) - (Area of canvas wasted).

=551 sq m - 1 sq m

=550 sq m

Now, let the slant height be l m.

Therefore, curved surface area =πrl

=(22/7)(7)l

Thus,

(22/7)(7)l = 550

=> l = (550×7)/(22×7)

=> l = 25

We have; height=√(l^2 - r^2)

=√(25^2-7^2) m

=√{(25+7)×(25-7)} m

=√(576) m

=24 m

Therefore, volume of the cone =(1/3)π(r^2)h

=(1/3)×(22/7)×(7×7)×24 sq m.

=1232 sq m. [Answer]

Hope This Helps You!!!