Question 8
10 pts
One of the values $r$ (radius), $d$ (diameter), $V$ (volume), or $S$ (surface area) is given for a particular sphere. Find the indicated value. Leave $π$ in your answer.
$V = 972 π {cm}^{3}; r = ?$
$12 cm$
$3 cm$
$729 cm$
$9 cm$

Answer

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Answer

$9 cm$ is the final answer.

Steps

Step 1 ：Given the volume of the sphere $V = 972 π {cm}^{3}$ , we are asked to find the radius $r$ .

Step 2 ：The formula for the volume of a sphere is $V = \frac{4}{3} π r^{3}$ . We can rearrange this formula to solve for $r$ : $r = {(\frac{3 V}{4 π})}^{\frac{1}{3}}$ .

Step 3 ：Substitute the given volume into the formula: $r = {(\frac{3 \times 972 π}{4 π})}^{\frac{1}{3}}$ .

Step 4 ：Simplify the expression to find the radius: $r \approx 9 cm$ .

Step 5 ： $9 cm$ is the final answer.

Question 810 ptsOne of the values r (radius), d (diameter), V (volume), or S (surface area) is given for a particular sphere. Find the indicated value. Leave π in your answer.V=972πcm3;r=?12 cm3 cm729 cm9 cm

Answer

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Question 8
10 pts
One of the values $r$ (radius), $d$ (diameter), $V$ (volume), or $S$ (surface area) is given for a particular sphere. Find the indicated value. Leave $π$ in your answer.
$V = 972 π {cm}^{3}; r = ?$
$12 cm$
$3 cm$
$729 cm$
$9 cm$