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A Cylindrical Bucket of Diameter 28 Cm and Height 20 Cm Was Full of Sand. When the Sand in the Bucket Was Poured on the Ground, the Sand Got Converted into a Shape of a Cone. - SSC (Marathi Semi-English) 10th - Geometry

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Question

A cylindrical bucket of diameter 28 cm and height 20 cm was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was 14 cm, what was the base area of the cone ?

Solution

Radius of the bucket, r = \[\frac{28}{2}\]= 14 cm
Height of the bucket, h = 20 cm
Height of the cone, H = 14 cm
Let the radius of the base of the cone be R cm.
∴ Area of the base of the cone =  \[\pi\]R2

Now,
Volume of sand in the cone = Volume of sand in the cylindrical bucket

\[\therefore \frac{1}{3}\pi R^2 H = \pi r^2 h\]
\[ \Rightarrow \pi R^2 = \frac{3\pi r^2 h}{H}\]
\[ \Rightarrow \pi R^2 = \frac{3 \times \frac{22}{7} \times \left( 14 \right)^2 \times 20}{14}\]
\[ \Rightarrow \pi R^2 = 2640 {cm}^2\]

Thus, the base area of the cone is 2640 cm2.

 
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Solution A Cylindrical Bucket of Diameter 28 Cm and Height 20 Cm Was Full of Sand. When the Sand in the Bucket Was Poured on the Ground, the Sand Got Converted into a Shape of a Cone. Concept: Surface Area of a Combination of Solids.
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