A can of soda can be modeled as a right cylinder. Mia measures its height as 9.3 cm and its circumference as 14.1 cm. Find the volume of the can in cubic centimeters. Round your answer to the nearest tenth if necessary.
The Correct Answer and Explanation is:
To find the volume of the soda can modeled as a right cylinder, we can use the formula for the volume of a cylinder:V=πr2hV = \pi r^2 hV=πr2h
Where:
- VVV is the volume of the cylinder,
- rrr is the radius of the base,
- hhh is the height of the cylinder,
- π≈3.1416\pi \approx 3.1416π≈3.1416.
Step 1: Find the radius of the base
We are given the circumference of the can, which is 14.1 cm. The formula for the circumference of a circle is:C=2πrC = 2\pi rC=2πr
Rearranging to solve for rrr:r=C2πr = \frac{C}{2\pi}r=2πC
Substitute the given circumference:r=14.12π=14.16.2832≈2.24 cmr = \frac{14.1}{2\pi} = \frac{14.1}{6.2832} \approx 2.24 \, \text{cm}r=2π14.1=6.283214.1≈2.24cm
Step 2: Calculate the volume
Now that we have the radius (r≈2.24 cmr \approx 2.24 \, \text{cm}r≈2.24cm) and the height (h=9.3 cmh = 9.3 \, \text{cm}h=9.3cm), we can plug these values into the volume formula:V=π(2.24)2(9.3)V = \pi (2.24)^2 (9.3)V=π(2.24)2(9.3)V=3.1416×5.0176×9.3≈3.1416×46.69≈146.45 cubic centimetersV = 3.1416 \times 5.0176 \times 9.3 \approx 3.1416 \times 46.69 \approx 146.45 \, \text{cubic centimeters}V=3.1416×5.0176×9.3≈3.1416×46.69≈146.45cubic centimeters
Step 3: Round the answer
To the nearest tenth, the volume is approximately:V≈146.5 cubic centimetersV \approx 146.5 \, \text{cubic centimeters}V≈146.5cubic centimeters
Thus, the volume of the can is 146.5 cubic centimeters.
