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A frustum of a cone is of height 12cm with radii of its circular ends as 2cm and 4cm. The volume of the frustum is
- a)354cm3
- b)350cm3
- c)352cm3
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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A frustum of a cone is of height 12cm with radii of its circular ends ...
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A frustum of a cone is of height 12cm with radii of its circular ends ...
To find the volume of the frustum of a cone, we can use the formula:
V = (1/3) * π * (R^2 + r^2 + R*r) * h
Where:
V = Volume of the frustum
π = Pi (approximately 3.14159)
R = Radius of the larger circular end
r = Radius of the smaller circular end
h = Height of the frustum
Given:
Height of the frustum (h) = 12 cm
Radius of the larger circular end (R) = 4 cm
Radius of the smaller circular end (r) = 2 cm
Now, let's substitute the given values into the formula and calculate the volume:
V = (1/3) * π * (4^2 + 2^2 + 4*2) * 12
V = (1/3) * π * (16 + 4 + 8) * 12
V = (1/3) * π * 28 * 12
V = (1/3) * 3.14159 * 28 * 12
V = (1/3) * 3.14159 * 336
V = 3.14159 * 112
V ≈ 352 cm^3
Therefore, the volume of the frustum is approximately 352 cm^3, which matches with option C.
V = (1/3) * π * (R^2 + r^2 + R*r) * h
Where:
V = Volume of the frustum
π = Pi (approximately 3.14159)
R = Radius of the larger circular end
r = Radius of the smaller circular end
h = Height of the frustum
Given:
Height of the frustum (h) = 12 cm
Radius of the larger circular end (R) = 4 cm
Radius of the smaller circular end (r) = 2 cm
Now, let's substitute the given values into the formula and calculate the volume:
V = (1/3) * π * (4^2 + 2^2 + 4*2) * 12
V = (1/3) * π * (16 + 4 + 8) * 12
V = (1/3) * π * 28 * 12
V = (1/3) * 3.14159 * 28 * 12
V = (1/3) * 3.14159 * 336
V = 3.14159 * 112
V ≈ 352 cm^3
Therefore, the volume of the frustum is approximately 352 cm^3, which matches with option C.
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A frustum of a cone is of height 12cm with radii of its circular ends as 2cm and 4cm. The volume of the frustum isa)354cm3b)350cm3c)352cm3d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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