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The radius of a right circular cone of height 6 cm and volume 77 cm3 is
- a)3.5 cm
- b)2 cm
- c)3 cm
- d)4 cm
Correct answer is option 'A'. Can you explain this answer?
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The radius of a right circular cone of height 6 cm and volume 77 cm3is...
To find the radius of a right circular cone, we need to use the formula for the volume of a cone and solve for the radius. The formula for the volume of a cone is given by:
V = (1/3) * π * r^2 * h
where V is the volume, π is approximately 3.14159, r is the radius, and h is the height.
Given that the height of the cone is 6 cm and the volume is 77 cm^3, we can substitute these values into the formula and solve for the radius.
1. Write down the given information:
- Height (h) = 6 cm
- Volume (V) = 77 cm^3
2. Substitute the values into the formula:
77 = (1/3) * 3.14159 * r^2 * 6
3. Simplify the equation:
77 = 0.5236 * r^2 * 6
4. Divide both sides of the equation by 0.5236 * 6:
77 / (0.5236 * 6) = r^2
5. Simplify the equation:
77 / 3.14159 = r^2
6. Take the square root of both sides to solve for r:
√(77 / 3.14159) = r
7. Use a calculator to find the value of r:
r ≈ 3.5 cm
Therefore, the radius of the right circular cone is approximately 3.5 cm. So, the correct answer is option A - 3.5 cm.
V = (1/3) * π * r^2 * h
where V is the volume, π is approximately 3.14159, r is the radius, and h is the height.
Given that the height of the cone is 6 cm and the volume is 77 cm^3, we can substitute these values into the formula and solve for the radius.
1. Write down the given information:
- Height (h) = 6 cm
- Volume (V) = 77 cm^3
2. Substitute the values into the formula:
77 = (1/3) * 3.14159 * r^2 * 6
3. Simplify the equation:
77 = 0.5236 * r^2 * 6
4. Divide both sides of the equation by 0.5236 * 6:
77 / (0.5236 * 6) = r^2
5. Simplify the equation:
77 / 3.14159 = r^2
6. Take the square root of both sides to solve for r:
√(77 / 3.14159) = r
7. Use a calculator to find the value of r:
r ≈ 3.5 cm
Therefore, the radius of the right circular cone is approximately 3.5 cm. So, the correct answer is option A - 3.5 cm.
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The radius of a right circular cone of height 6 cm and volume 77 cm3isa)3.5 cmb)2 cmc)3 cmd)4 cmCorrect answer is option 'A'. Can you explain this answer?
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