Question

approximately how much ice cream is in this cone shown below? assume the cone is completely filled and the dome is approximated as a hemisphere. use 3.1416 for the approximate value of π. round your answer to two decimal places, as needed. volume = \boxed{} cm³ of ice cream. image of ice cream cone with radius 5 cm (dotted line) and cone height 17.5 cm

Explanation:

Step1: Calculate volume of cone

The formula for the volume of a cone is $V_{cone} = \frac{1}{3}\pi r^2 h$. Here, $r = 5$ cm and $h = 17.5$ cm, $\pi = 3.1416$.
$V_{cone} = \frac{1}{3} \times 3.1416 \times 5^2 \times 17.5$
$= \frac{1}{3} \times 3.1416 \times 25 \times 17.5$
$= \frac{1}{3} \times 3.1416 \times 437.5$
$= \frac{1374.45}{3}$
$= 458.15$

Step2: Calculate volume of hemisphere

The formula for the volume of a hemisphere is $V_{hemisphere} = \frac{2}{3}\pi r^3$. Here, $r = 5$ cm, $\pi = 3.1416$.
$V_{hemisphere} = \frac{2}{3} \times 3.1416 \times 5^3$
$= \frac{2}{3} \times 3.1416 \times 125$
$= \frac{785.4}{3}$
$= 261.8$

Step3: Total volume of ice cream

Add the volume of the cone and the hemisphere.
$V_{total} = V_{cone} + V_{hemisphere}$
$= 458.15 + 261.8$
$= 719.95$

Answer:

719.95