Question

determine the volume of the cylinder. leave the answer in terms of \\(\pi\\).

hint: use the formula sheet to determine the formula(s) needed to solve the problem.

a: \\(21\pi\text{ ft}^3\\)
b: \\(63\pi\text{ ft}^3\\)
c: \\(9\pi\text{ ft}^3\\)
d: \\(60\pi\text{ ft}^3\\)

Explanation:

🆕 New Concept Discovered: Calculating Volume of Cylinders
Multiply circular base area by height

Step 1: Identify the formula and given values

The volume \( V \) of a cylinder is calculated by multiplying the area of its circular base by its height:

$$ V = \pi r^2 h $$

From the given image:

• Radius of the circular base, \( r = 3\text{ ft} \)
• Height of the cylinder, \( h = 7\text{ ft} \)

Step 2: Substitute the values into the formula

Substitute \( r = 3 \) and \( h = 7 \) into the volume formula:

$$ V = \pi \cdot (3)^2 \cdot 7 $$

Step 3: Simplify the expression

Calculate the square of the radius and multiply by the height:

$$ V = \pi \cdot 9 \cdot 7 $$

$$ V = 63\pi\text{ ft}^3 $$

Answer:

B \( 63\pi\text{ ft}^3 \)