Question

what is the volume of this cylinder?
round your answer to the nearest hundredth.
image of a cylinder with radius 12 cm and height 8 cm
options: 3,617.28; 7234.56; 10851.84; 1808.64

a cylinder has a height of 16 meters and a radius of 9 meters. what is its volume? round your answer to the nearest hundredth.
options: 4,069.44; 2034.72; 1017.36; 508.68

Explanation:

First Question (Cylinder with radius 12 cm, height 8 cm)

Step1: Recall cylinder volume formula

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute values

Here, \( r = 12 \) cm, \( h = 8 \) cm, and \( \pi \approx 3.14 \). So, \( V = 3.14 \times 12^2 \times 8 \).

Step3: Calculate \( 12^2 \)

\( 12^2 = 144 \).

Step4: Multiply step by step

First, \( 3.14 \times 144 = 452.16 \). Then, \( 452.16 \times 8 = 3617.28 \).

Step1: Use cylinder volume formula

\( V = \pi r^2 h \), with \( r = 9 \) m, \( h = 16 \) m, \( \pi \approx 3.14 \).

Step2: Substitute and calculate \( r^2 \)

\( r^2 = 9^2 = 81 \).

Step3: Multiply by \( \pi \) and \( h \)

\( V = 3.14 \times 81 \times 16 \). First, \( 3.14 \times 81 = 254.34 \). Then, \( 254.34 \times 16 = 4069.44 \).

Answer:

3,617.28 (the first option)

Second Question (Cylinder with radius 9 m, height 16 m)