Question

for problems 5–6, find the volume of each cylinder. use 3.14 for $\pi$. round the volume to the nearest tenth.

1. image of a cylinder with radius 1.8 m and height 5.1 m
2. image of a cylinder with diameter 4.2 cm and height 1.7 cm

Explanation:

Problem 5:

Step1: Recall cylinder volume formula

The formula for the volume \( V \) of a cylinder is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We are given \( \pi = 3.14 \), \( r = 1.8 \, \text{m} \), and \( h = 5.1 \, \text{m} \).

Step2: Calculate \( r^2 \)

First, find \( r^2 \): \( r^2=(1.8)^2 = 3.24 \).

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

Now, substitute into the formula: \( V = 3.14\times3.24\times5.1 \).
First, calculate \( 3.14\times3.24 = 10.1736 \).
Then, multiply by \( 5.1 \): \( 10.1736\times5.1 = 51.88536 \).

Step4: Round to nearest tenth

Rounding \( 51.88536 \) to the nearest tenth gives \( 51.9 \).

Step1: Recall cylinder volume formula and find radius

The formula for the volume \( V \) of a cylinder is \( V=\pi r^2 h \). The diameter is given as \( 4.2 \, \text{cm} \), so the radius \( r=\frac{4.2}{2}=2.1 \, \text{cm} \). We know \( \pi = 3.14 \) and \( h = 1.7 \, \text{cm} \).

Step2: Calculate \( r^2 \)

Find \( r^2 \): \( r^2=(2.1)^2 = 4.41 \).

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

Substitute into the formula: \( V = 3.14\times4.41\times1.7 \).
First, calculate \( 3.14\times4.41 = 13.8474 \).
Then, multiply by \( 1.7 \): \( 13.8474\times1.7 = 23.54058 \).

Step4: Round to nearest tenth

Rounding \( 23.54058 \) to the nearest tenth gives \( 23.5 \).

Answer:

The volume of the cylinder in Problem 5 is \( \boldsymbol{51.9} \) cubic meters.

Problem 6: