A cylindrical bucket of diameter 42 cm and height 10 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 21 cm, what was the base area of the cone?

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A cylindrical bucket of diameter 42 cm and height 10 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 21 cm, what was the base area of the cone?

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Kerala PSC Common Preliminary Exam (GRADUATE LEVEL) PYP 38-24

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1980 cm2
2015 cm2
1780 cm2
2036 cm2

Answer 1

Ans: (A) 1980 cm2

Key Points : Volume of the cylinder:

Radius of the cylinder (r) = Diameter / 2 = 42 cm / 2 = 21 cm

Height of the cylinder (h) = 10 cm

Volume of cylinder = πr²h = π * (21)² * 10 = π * 441 * 10 = 4410π cm³

Important Points :

Volume of the cone: The volume of the sand remains the same when poured from the cylinder to the cone.

Volume of cone = (1/3)πR²H, where R is the radius of the cone's base and H is the cone's height.

Height of the cone (H) = 21 cm

Equate the volumes and solve for the base area:

4410π = (1/3)πR² * 21

4410π = 7πR²

R² = 4410π / 7π

R² = 630 cm²

The base area of the cone is πR². We already found R² to be 630. Therefore, the base area is 630π. If we use π ≈ 22/7, the base area is (22/7) * 630 = 22 * 90 = 1980 cm².

Additional Information :

Volume of Cylinder: You correctly calculated the volume of the cylinder as πr²h = π * (21)² * 10 = 4410π cm³.

Volume of Cone: The volume of the cone is (1/3)πR²H, where R is the radius of the cone's base and H is the cone's height.

Equating Volumes: You correctly equated the volumes: 4410π = (1/3)πR² * 21.

Solving for R²: Your calculation of R² is also correct: R² = 630 cm².

Base Area of the Cone: The base area of the cone is indeed πR². Since you've already found R², the base area is simply 630π cm².

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A cylindrical bucket of diameter 42 cm and height 10 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 21 cm, what was the base area of the cone?

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