Question

a large spoon is used for serving soup. the part of the spoon that holds the soup is in the shape of a hemisphere (half of a sphere) with diameter 4 inches. which is closest to the amount of soup the spoon can hold? (use $\pi = 3.14$ )
$\bigcirc$ $16.1\\ \text{in}^3$

$\bigcirc$ $19.7\\ \text{in}^3$

$\bigcirc$ $33.5\\ \text{in}^3$

$\bigcirc$ $16.7\\ \text{in}^3$

$\bigcirc$ $8.4\\ \text{in}^3$

Explanation:

Step1: Find the radius of the hemisphere

The diameter of the hemisphere is 4 inches, so the radius \( r=\frac{4}{2} = 2 \) inches.

Step2: Recall the formula for the volume of a hemisphere

The volume \( V \) of a hemisphere is given by the formula \( V=\frac{2}{3}\pi r^{3} \).

Step3: Substitute the values of \( \pi \) and \( r \) into the formula

Substitute \( \pi = 3.14 \) and \( r = 2 \) into the formula:
\[

$$\begin{align*} V&=\frac{2}{3}\times3.14\times(2)^{3}\\ &=\frac{2}{3}\times3.14\times8\\ &=\frac{2\times3.14\times8}{3}\\ &=\frac{50.24}{3}\\ &\approx16.7 \text{ cubic inches} \end{align*}$$

\]

Answer:

16.7 in³