Math, asked by vksurya218, 11 hours ago

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.

Answers

Answered by RitaNarine
0

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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