Final answer:
The volume of the right cylindrical coffee can is calculated using the formula V = πr²h and the measurements provided for the radius and height. After plugging in the correct values and performing the calculation, the volume is found in cubic inches and rounded to the nearest tenth as necessary.
Step-by-step explanation:
The question involves finding the volume of a right cylindrical can of ground coffee, using the measurements provided for its height and radius. To calculate the volume in cubic inches, the formula V = πr²h is used, where V is volume, r is radius, and h is height. Given the radius as \(\frac{3}{4} in\) and height as 5\(\frac{1}{4}\) in, we plug these values into the formula to compute the volume.
First, we convert the radius and height to decimal form:
- Radius = \(\frac{3}{4} in = 0.75 in\)
- Height = 5\(\frac{1}{4}\) in = 5.25 in
Next, we apply the formula:
V = π(0.75 in)²(5.25 in) = π(0.5625 in²)(5.25 in) = π(2.953125 in³)
Assuming π is approximately 3.14159, we get:
V ≈ 3.14159 × 2.953125 in³ ≈ 9.278 in³
However, the example provided contains a calculation error, and we would need to correct the value of volume after applying the exact radius and height into the correct formula for volume of a cylinder. The corrected value should be rounded to the nearest tenth following mathematical rounding rules.