Final answer:
To calculate the height of the waste can, use the volume of a cylinder formula V = πr²h, rearrange to find h, and then solve the formula with the given volume and area of the base rounded to the nearest tenth.
Step-by-step explanation:
To find the height of a cylindrical waste can, we need to use the formula for the volume of a cylinder which is V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. In this case, we are given the volume (V = 2474 cubic inches) and the area of the base (A = 177 square inches).
The area of the base is also given by the formula A = πr², so to find the height, we first solve for r using the area to find the radius and then rearrange the volume formula to solve for h (height): h = V/A. After substituting the given values into the formula, we calculate the height and round it to the nearest tenth.
The calculation steps would be:
- Find the radius of the base using the area: r = √(A/π).
- Substitute the values into the height formula: h = V/A.
- Calculate h and round to the nearest tenth.