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A Washing Tub in the Shape of a Frustum of a Cone Has a Height of 21 Cm. the Radii of the Circular Top and Bottom Are 20 Cm and 15 Cm Respectively.What is the Capacity of the Tub? ( π = 22 7 ). - Geometry

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Question

A washing tub in the shape of a frustum of a cone has a height of 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub? ( \[\pi = \frac{22}{7}\]).

Solution

Radius of the circular top of washing tub, r1 = 20 cm
Radius of the circular bottom of washing tub, r2 = 15 cm
Height of the washing tub, h = 21 cm 
∴ Capacity of the washing tub = Volume of frustum of cone

\[= \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]
\[ = \frac{1}{3} \times \frac{22}{7} \times 21 \times \left( {20}^2 + 20 \times 15 + {15}^2 \right)\]
\[ = 22 \times \left( 400 + 300 + 225 \right)\]
\[ = 22 \times 925\]
\[ = 20350 {cm}^3\]

\[= \frac{20350}{1000} L \left( 1 L = 1000 {cm}^3 \right)\]
\[ = 20 . 35 L\]

Thus, the capacity of the tub is 20.35 litres.

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A Washing Tub in the Shape of a Frustum of a Cone Has a Height of 21 Cm. the Radii of the Circular Top and Bottom Are 20 Cm and 15 Cm Respectively.What is the Capacity of the Tub? ( π = 22 7 ). Concept: Frustum of a Cone.
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