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V=(4)/(3)pir^(3)
The formula gives the volume 
V of a sphere with radius 
r. What is the volume, in cubic inches, of a sphere with a radius of 6 inches?
Choose 1 answer:
(A) 
864 pi
(B) 
288 pi
(C) 
216 pi
(D) 
48 pi

V=43πr3 V=\frac{4}{3} \pi r^{3} \newlineThe formula gives the volume V V of a sphere with radius r r . What is the volume, in cubic inches, of a sphere with a radius of 66 inches?\newlineChoose 11 answer:\newline(A) 864π 864 \pi \newline(B) 288π 288 \pi \newline(C) 216π 216 \pi \newline(D) 48π 48 \pi

Full solution

Q. V=43πr3 V=\frac{4}{3} \pi r^{3} \newlineThe formula gives the volume V V of a sphere with radius r r . What is the volume, in cubic inches, of a sphere with a radius of 66 inches?\newlineChoose 11 answer:\newline(A) 864π 864 \pi \newline(B) 288π 288 \pi \newline(C) 216π 216 \pi \newline(D) 48π 48 \pi
  1. Volume formula for a sphere: The formula for the volume of a sphere is given by V=43πr3 V = \frac{4}{3} \pi r^3 . To find the volume of a sphere with a radius of 66 inches, we need to substitute r=6 r = 6 into the formula.
  2. Substitute radius into the formula: Substitute r=6 r = 6 into the volume formula: V=43π(6)3 V = \frac{4}{3} \pi (6)^3 .
  3. Calculate the volume: Calculate the volume using the substituted values: V=43π(6)3=43π(216) V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) because 63=6×6×6=216 6^3 = 6 \times 6 \times 6 = 216 .
  4. Multiply by 43 \frac{4}{3} : Multiply 43 \frac{4}{3} by 216 216 to get the volume: V=43×216π=4×72π V = \frac{4}{3} \times 216 \pi = 4 \times 72 \pi .
  5. Final volume calculation: Calculate the final volume: V=4×72π=288π V = 4 \times 72 \pi = 288 \pi cubic inches.

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