Question 37 asks to find the sum of the interior angles of a pentagon. Question 38 asks to calculate the volume of a sphere with diameter 12 cm, using $\pi = \frac{22}{7}$, and to round the answer to the nearest cubic centimeter.

1. Problem Description

Question 37 asks to find the sum of the interior angles of a pentagon.

Question 38 asks to calculate the volume of a sphere with diameter 12 cm, using $\pi = \frac{22}{7}$, and to round the answer to the nearest cubic centimeter.

2. Solution Steps

Question 37:

The formula for the sum of the interior angles of a polygon with $n$ sides is:

$S = (n-2) \times 180^\circ$

For a pentagon, $n = 5$, so the sum of its interior angles is:

$S = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$

Question 38:

The volume of a sphere is given by the formula:

$V = \frac{4}{3} \pi r^3$

The diameter of the sphere is 12 cm, so the radius is $r = \frac{12}{2} = 6$ cm.

Given $\pi = \frac{22}{7}$, the volume of the sphere is:

$V = \frac{4}{3} \times \frac{22}{7} \times 6^3 = \frac{4}{3} \times \frac{22}{7} \times 216 = \frac{4 \times 22 \times 72}{7} = \frac{6336}{7} \approx 905.142857$

Rounding to the nearest cubic centimeter, we get 905 $cm^3$.

3. Final Answer

Question 37: C. 540°

Question 38: C. 905 $cm^3$