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Question

Part 1
The volume of a cylinder is 1421pi cmcubed. The height of the cylinder is 29 cm. What is the radius of the​ cylinder?

Answer 1

To find the radius of a cylinder, we can use the formula for the volume of a cylinder:

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

Where:

• $V$ is the volume,
• $r$ is the radius, and
• $h$ is the height.

We are given:

• $V=1421\pi$ cm³
• $h=29$ cm

We can plug in the values into the volume formula:

$$1421\pi =\pi r^2(29)$$

First, we'll divide both sides by $\pi$:

$$1421=r^2\cdot 29$$

Now, divide both sides by 29 to solve for $r^2$:

$$r^2=\frac{1421}{29}$$

Calculating the right side:

$$r^2=49$$

Now, take the square root of both sides to find $r$:

$$r=\sqrt{49}=7$$

Therefore, the radius of the cylinder is $\boxed{{\displaystyle 7}}$ cm.