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What is the volume of a cylinder with a height of 11.7 in and a base with a diameter of 10.6 in, to the nearest tenth of a cubic inch? Answer: in ^(3)

What is the volume of a cylinder with a height of 1111.77 in\text{in} and a base with a diameter of 1010.66 in\text{in}, to the nearest tenth of a cubic inch?\newlineAnswer: in\text{in} 3 ^{3}

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Q. What is the volume of a cylinder with a height of 1111.77 in\text{in} and a base with a diameter of 1010.66 in\text{in}, to the nearest tenth of a cubic inch?\newlineAnswer: in\text{in} 3 ^{3}
  1. Identify formula: Identify the formula for the volume of a cylinder.\newlineThe formula for the volume of a cylinder is V=πr2hV = \pi r^2 h, where rr is the radius of the base and hh is the height of the cylinder.
  2. Calculate radius: Calculate the radius of the base of the cylinder.\newlineThe diameter of the base is given as 10.610.6 inches. The radius is half of the diameter, so r=diameter/2=10.6 inches/2r = \text{diameter} / 2 = 10.6 \text{ inches} / 2.
  3. Perform calculation: Perform the calculation for the radius. r=10.6 inches2=5.3 inchesr = \frac{10.6 \, \text{inches}}{2} = 5.3 \, \text{inches}.
  4. Substitute values: Substitute the radius and height into the volume formula.\newlineUsing the radius r=5.3r = 5.3 inches and height h=11.7h = 11.7 inches, the volume formula becomes V=π×(5.3 inches)2×11.7 inchesV = \pi \times (5.3 \text{ inches})^2 \times 11.7 \text{ inches}.
  5. Calculate volume: Calculate the volume using the substituted values.\newlineV=π×(5.3 inches)2×11.7 inches=π×28.09 inches2×11.7 inches.V = \pi \times (5.3 \, \text{inches})^2 \times 11.7 \, \text{inches} = \pi \times 28.09 \, \text{inches}^2 \times 11.7 \, \text{inches}.
  6. Perform multiplication: Perform the multiplication to find the volume.\newlineV≈3.14159×28.09 inches2×11.7 inches=1031.0173 cubic inches.V \approx 3.14159 \times 28.09 \text{ inches}^2 \times 11.7 \text{ inches} = 1031.0173 \text{ cubic inches}.
  7. Round volume: Round the volume to the nearest tenth of a cubic inch. V≈1031.0V \approx 1031.0 cubic inches.

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