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V=(1)/(3)pir^(2)h
The formula gives the volume 
V of a right circular cone with radius 
r and height 
h. What is the volume, in cubic inches, of a right circular cone with a radius of 12 inches and a height of 2 inches?
Choose 1 answer:
(A) 
96 pi
(B) 
72 pi
(c) 
24 pi
(D) 
8pi

V=13πr2h V=\frac{1}{3} \pi r^{2} h \newlineThe formula gives the volume V V of a right circular cone with radius r r and height h h . What is the volume, in cubic inches, of a right circular cone with a radius of 1212 inches and a height of 22 inches?\newlineChoose 11 answer:\newline(A) 96π 96 \pi \newline(B) 72π 72 \pi \newline(C) 24π 24 \pi \newline(D) 8π 8 \pi

Full solution

Q. V=13πr2h V=\frac{1}{3} \pi r^{2} h \newlineThe formula gives the volume V V of a right circular cone with radius r r and height h h . What is the volume, in cubic inches, of a right circular cone with a radius of 1212 inches and a height of 22 inches?\newlineChoose 11 answer:\newline(A) 96π 96 \pi \newline(B) 72π 72 \pi \newline(C) 24π 24 \pi \newline(D) 8π 8 \pi
  1. Substitute given values: The formula for the volume of a right circular cone is V=13πr2h V = \frac{1}{3}\pi r^2 h . We need to substitute the given values for the radius (r=12 r = 12 inches) and height (h=2 h = 2 inches) into the formula to find the volume.
  2. Calculate square of radius: First, calculate the square of the radius: r2=(12 inches)2=144 inches2r^2 = (12 \text{ inches})^2 = 144 \text{ inches}^2.
  3. Multiply by height: Next, multiply the result by the height: r2h=144 inches2×2 inches=288 inches3r^2h = 144 \text{ inches}^2 \times 2 \text{ inches} = 288 \text{ inches}^3.
  4. Include π\pi: Now, multiply this result by π\pi to include the π\pi from the formula: πr2h=π×288 inches3\pi r^2 h = \pi \times 288 \text{ inches}^3.
  5. Multiply by (13)(\frac{1}{3}): Finally, multiply by the fraction (13)(\frac{1}{3}) to complete the formula: V=(13)πr2h=(13)×π×288 inches3V = (\frac{1}{3})\pi r^2h = (\frac{1}{3}) \times \pi \times 288 \text{ inches}^3.
  6. Perform multiplication: Perform the multiplication: V=(13)×288π inches3=96π inches3V = \left(\frac{1}{3}\right) \times 288\pi \text{ inches}^3 = 96\pi \text{ inches}^3.

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