Monica has a piece of Canvas whose area is 551 m2. She uses it to have

1.	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 wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.
Answer» We have, Area of canvas = 551 m² Area of canvas lost in wastage = 1 m² ∴ Area of canvas used in making tent = (551-1) m² = 550 m² = Surface area of the cone = 550 m² We have, r = radius of the base of the cone = 7 m ∴ Surface area = 550 m² = πrl = 550 = \(\frac{22}{7}\)×7×l = 550 = l = 25 m Let h be the height of the cone. Then, l² = r²+ h² = h = \(\sqrt{l^2-r^2}\) = \(\sqrt{25^2-7^2}\) = 24 m ∴ Volume of the cone = \(\frac{1}{3}\)πr²h = \(\frac{1}{3}\) ×\(\frac{22}{7}\)×7×7×24m³ = 1232 m³

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 wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.

Answer»

We have,

Area of canvas = 551 m²

Area of canvas lost in wastage = 1 m²

∴ Area of canvas used in making tent

= (551-1) m² = 550 m²

= Surface area of the cone = 550 m²

We have,

r = radius of the base of the cone = 7 m

∴ Surface area = 550 m²

= πrl = 550

= \(\frac{22}{7}\)×7×l = 550

= l = 25 m

Let h be the height of the cone.

Then,

l² = r²+ h²

= h = \(\sqrt{l^2-r^2}\)

= \(\sqrt{25^2-7^2}\)

= 24 m

∴ Volume of the cone = \(\frac{1}{3}\)πr²h

= \(\frac{1}{3}\) ×\(\frac{22}{7}\)×7×7×24m³

= 1232 m³