A cylinder has a base diameter of 10cm and a height of 14cm. What is its volume in cubic cm, to the nearest tenths place?

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

$V = \pi r^2 h$

where $V$ is the volume, $r$ is the radius of the base, and $h$ is the height of the cylinder.

1. First, determine the radius of the base. The diameter is given as 10 cm, so the radius $r$ is half of the diameter:

$r = \frac{10 \text{ cm}}{2} = 5 \text{ cm}$

2. The height $h$ is given as 14 cm.

3. Substitute the values of $r$ and $h$ into the volume formula:

$V = \pi (5 \text{ cm})^2 (14 \text{ cm})$

4. Calculate the square of the radius:

$(5 \text{ cm})^2 = 25 \text{ cm}^2$

5. Multiply by the height:

$25 \text{ cm}^2 \times 14 \text{ cm} = 350 \text{ cm}^3$

6. Multiply by $\pi$ (using $\pi \approx 3.14159$):

$V \approx 350 \text{ cm}^3 \times 3.14159 \approx 1099.56 \text{ cm}^3$

7. Round to the nearest tenths place:

$V \approx 1099.6 \text{ cm}^3$

So, the volume of the cylinder is approximately 1099.6 cubic cm.