Example 16
Monica has a piece of canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it.
Let tent have radius = r = 7m
Let slant height = l m
Let height = h m
Area of canvas = Area available for making tent + Wastage
551 m2 = Area available for making tent + 1 m2
Area available for making tent = 551 m2 – 1 m2 = 550 m2
Area available for making tent = Curved surface area of conical tent
550 = πrl
550 = 22/7 × 7 × l
550 = 22 × 1 × l
22 × 1 × l = 550
l = 550/22 m
l = 25 m
We know that
l2 = h2 + r2
252 = h2 + 72
252 – 72 = h2
h2 = 252 – 72
h2 = (25 – 7) (25 + 7)
h2 = (18) (32)
h = √("18(32)" )
h = √("(9 × 2) × (32)" )
h = √("(9) × (64)" )
h = √("(32) × (82)" )
h = 3 × 8
h = 24 m
Volume of tent = 1/3πr2h
= 1/3 × 22/7 × 7 × 7 × 24 m3
= 22 × 1 × 7 × 8 m3
= 1232 m3.

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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