Question

what is the volume of this sphere? round your answer to the nearest hundredth. sphere image with 72 cm (presumably radius or diameter) blank cubic centimeters submit

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume \( V \) of a sphere is \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere. From the diagram, the radius \( r = 72\space\text{cm}\).

Step2: Substitute the radius into the formula

Substitute \( r = 72 \) into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\pi(72)^{3}\\ &=\frac{4}{3}\pi\times72\times72\times72\\ &=\frac{4}{3}\pi\times373248\\ & = 4\times124416\times\pi\\ &=497664\pi \end{align*}$$

\]

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have:
\[
V\approx497664\times3.14159
\]
\[
V\approx497664\times3 + 497664\times0.14159
\]
\[
V\approx1492992+70460.0
\]
\[
V\approx1563452.0
\]
(More accurately, \( 497664\times3.14159 = 497664\times3+497664\times0.14159=1492992 + 497664\times0.1+497664\times0.04+497664\times0.00159\)
\(=1492992+49766.4 + 19906.56+791.28576\)
\(=1492992+49766.4=1542758.4+19906.56 = 1562664.96+791.28576=1563456.24576\))

Step4: Round to the nearest hundredth

The value \( 1563456.24576 \) rounded to the nearest hundredth is \( 1563456.25 \) (since the thousandth digit is 5, we round up the hundredth digit).

Answer:

\( 1563456.25 \)