Question

You and your friend are building a snowman during winter break.You measure the snowman's head is 18 inches in diameter.What is the volumes of the snowman's head?

Answer 1

The volume of the snowman's head is calculated using the formula V = ⅓πr³. With a diameter of 18 inches, the radius is 9 inches, which results in a volume of approximately 4,188.79 cubic inches for the snowman's spherical head.

Step-by-step explanation:

To calculate the volume of the snowman's head, which has a spherical shape, we need to use the formula for the volume of a sphere. The formula is V = ⅓πr³, where V represents the volume, π (pi) is approximately 3.14159, and r is the radius of the sphere. In this case, the diameter of the snowman's head is given as 18 inches, so the radius r is half of that, which is 9 inches.

Now, plugging the radius into the formula,
V = ⅓π(9 inches)³
V = ⅓π(729 cubic inches)
V = 3.14159 × 729 cubic inches
V = approximately 4,188.79 cubic inches.

So the volume of the snowman's head is approximately 4,188.79 cubic inches. Remember, while calculators might give more decimal places, it's often more practical to round to two decimal places for ease of understanding, especially if the exactness isn't crucial for your needs.

Answer 2

The snowman's head has the shape of a sphere.

If the diameter is 18, then the radius is 18/2 = 9 in

The volume of a sphere is computed as follows:

`V=(4)/(3)\pi r^3`

where r is the radius. Replacing with r = 9:

`\begin{gathered} V=(4)/(3)\pi9^3 \\ V=972\pi \\ V=3053.63in^3 \end{gathered}`