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A tent has a cylindrical base with a conical top, the slant height of the conical part is 25 cm and the radius of the cylindrical base is 7 cm and the total height of the tent is 40 cm then what is the total volume of the tent?

A tent has a cylindrical base with a conical top, the slant height of the conical part is 25 cm and the radius of the cylindrical base is 7 cm and the total height of the tent is 40 cm then what is the total volume of the tent? Correct Answer 3696 cm<sup>3</sup>

Given:

Slant Height of Conical part (l) = 25 cm

Radius of the Cylindrical base (H) = 7 cm

Height of tent = 40 cm

Concept used:

As the conical top is over of the cylindrical base, the radius of both of them is equal

Formula Used:

Volume of Conical top = (1/3)(πr2h)

Volume of Cylindrical base = πr2H

Where:

r = radius of Conical top and Cylindrical base

h = height of Conical top

H = height of Cylindrical base

Calculations:

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Applying Pythagoras Theorem in conical top,

l2 = h2 + r2

⇒ (25)2 = h2 + (7)2

⇒ h2 = (25)2 - (7)2

⇒ h2 = 625 – 49

⇒ h2 = 576

Taking square root both side

⇒ h = √576

⇒ h = 24

Height of Cylindrical base (H) = 40 – 24 = 16

Volume of Tent = (1/3)(πr2h) + πr2H

⇒ {(1/3) × (22/7) × (7)2 × 24} + {(22/7) × (7)2 × 16}

⇒ {(1/3) × (22/7) × 49 × 24} + {(22/7) × 49 × 16}

⇒ 1232 + 2464 = 3696

∴ The Volume of Tent is 3696 cm3

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