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The radius and height of a right circular cone and that of a right circular cylinder are respectively equal. If the volume of the cylinder is 300 cu.cm, then the volume of the cone is
- a)300 cu.cm
- b)100 cu.cm
- c)600 cu.cm
- d)900 cu.cm
Correct answer is option 'B'. Can you explain this answer?
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The radius and height of a right circular cone and that of a right cir...
Let Radius and height of the cone be r and h respectively and Radius and height of the right circular cylinder be R and H.
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The radius and height of a right circular cone and that of a right cir...
Given:
- The radius and height of a right circular cone and a right circular cylinder are equal.
- The volume of the cylinder is 300 cu.cm.
To find:
- The volume of the cone.
Solution:
1. Let's assume that the radius and height of both the cone and the cylinder are 'r' cm.
2. The formula for the volume of a right circular cone is given by Vcone = (1/3)πr²h, where r is the radius and h is the height.
3. The formula for the volume of a right circular cylinder is given by Vcylinder = πr²h, where r is the radius and h is the height.
4. Since the radius and height of both the cone and the cylinder are equal, we can rewrite the formulas as Vcone = (1/3)πr³ and Vcylinder = πr³.
5. Given that the volume of the cylinder is 300 cu.cm, we have Vcylinder = 300.
6. Substituting the value of Vcylinder in the formula, we get πr³ = 300.
7. Dividing both sides of the equation by π, we get r³ = 300/π.
8. Taking the cube root of both sides, we get r = (300/π)^(1/3).
9. Now, substitute the value of r in the formula for the volume of the cone, Vcone = (1/3)πr³.
10. Substituting the value of r from step 8, we get Vcone = (1/3)π[(300/π)^(1/3)]³.
11. Simplifying the expression, we get Vcone = (1/3)π(300/π) = 100 cu.cm.
Therefore, the volume of the cone is 100 cu.cm. Hence, option B is correct.
- The radius and height of a right circular cone and a right circular cylinder are equal.
- The volume of the cylinder is 300 cu.cm.
To find:
- The volume of the cone.
Solution:
1. Let's assume that the radius and height of both the cone and the cylinder are 'r' cm.
2. The formula for the volume of a right circular cone is given by Vcone = (1/3)πr²h, where r is the radius and h is the height.
3. The formula for the volume of a right circular cylinder is given by Vcylinder = πr²h, where r is the radius and h is the height.
4. Since the radius and height of both the cone and the cylinder are equal, we can rewrite the formulas as Vcone = (1/3)πr³ and Vcylinder = πr³.
5. Given that the volume of the cylinder is 300 cu.cm, we have Vcylinder = 300.
6. Substituting the value of Vcylinder in the formula, we get πr³ = 300.
7. Dividing both sides of the equation by π, we get r³ = 300/π.
8. Taking the cube root of both sides, we get r = (300/π)^(1/3).
9. Now, substitute the value of r in the formula for the volume of the cone, Vcone = (1/3)πr³.
10. Substituting the value of r from step 8, we get Vcone = (1/3)π[(300/π)^(1/3)]³.
11. Simplifying the expression, we get Vcone = (1/3)π(300/π) = 100 cu.cm.
Therefore, the volume of the cone is 100 cu.cm. Hence, option B is correct.
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The radius and height of a right circular cone and that of a right circular cylinder are respectively equal. If the volume of the cylinder is 300 cu.cm, then the volume of the cone isa)300 cu.cmb)100 cu.cmc)600 cu.cmd)900 cu.cmCorrect answer is option 'B'. Can you explain this answer?
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