Cylinder A and cylinder B are mathematically similar. The length of cylinder A is 4 cm and the length of cylinder B is 6 cm. The volume of cylinder A is 80 cm3.
Calculate the volume of cylinder B.
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The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height.
- Since cylinder A and cylinder B are mathematically similar, their dimensions are proportional.
- Let's assume the radius of cylinder A is r cm. Then, the radius of cylinder B would be (r/4) * 6 cm, since the length of cylinder B is 6 cm, which is 1.5 times the length of cylinder A (6/4 = 1.5).
- We are given that the length of cylinder A is 4 cm and the volume of cylinder A is 80 cm^3. Using the formula for the volume of a cylinder, we can write:
- 80 = πr^2 * 4
- Simplifying, we have:
- 20 = πr^2
- Dividing both sides by π, we get:
- r^2 = 20/π
- Taking the square root of both sides, we find:
- r = √(20/π)
- Now, to calculate the volume of cylinder B, we use the same formula:
- V = π(r/4 * 6)^2 * 6
- Substituting the value of r, we have:
- V = π(√(20/π)/4 * 6)^2 * 6
- Calculating this expression will give us the volume of cylinder B.
- V = 30 cm^3
- Therefore, the volume of cylinder B is 30 cm^3.
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