Question

determine the approximate volume of the cylinder. round the answer to the nearest whole cubic yard. use \\(\pi \approx 3.14\\).

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

a. \\(9,236\text{ yd}^3\\)
b. \\(2,308\text{ yd}^3\\)
c. \\(660\text{ yd}^3\\)
d. \\(9,896\text{ yd}^3\\)

Explanation:

⚡ Using what you learned: volume of prisms, pyramids, cylinders, cones, spheres

Step 1: Identify the given dimensions

The cylinder has:

• A diameter \( d = 14\text{ yd} \), which means the radius \( r \) is:

$$ r = \frac{14}{2} = 7\text{ yd} $$

• A height (or length) \( h = 15\text{ yd} \)

Step 2: Calculate the volume

Using the volume formula for a cylinder:

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

Substitute the values \( r = 7 \), \( h = 15 \), and \( \pi \approx 3.14 \):

$$ V \approx 3.14 \times 7^2 \times 15 $$

$$ V \approx 3.14 \times 49 \times 15 $$

$$ V \approx 3.14 \times 735 $$

$$ V \approx 2307.9\text{ yd}^3 $$

Rounding to the nearest whole cubic yard gives \( 2,308\text{ yd}^3 \).

Answer:

B (2,308 yd³)