Question

Jessica was given the volume and the height of a cylinder. V= 43, h = 5.

She solved the formula for volume for r to find the radius of the cylinder.
Determine if Jessica solved the equation correctly and found the correct
answer. If not, describe what mistake she made, solve the formula for
correctly and justify your steps.
V=r2h
2v/rh=r
r= 5.47

Answer 1

Jessica incorrectly calculated the radius of a cylinder as 5.47. The correct method to find the radius from the volume is to divide the volume by the product of pi and the height, then take the square root, resulting in a radius of approximately 1.65.

Step-by-step explanation:

Jessica was given the volume (V) of a cylinder and its height (h). The formula for the volume of a cylinder is V = πr²h. With V= 43 and h = 5, to find the radius (r), we rearrange the formula to solve for r: r² = V/(πh).

Plugging in the given values, r² = 43/(3.14 · 5), which simplifies to r² = 43/15.7. Solving for r, we take the square root to get r ≈ 1.65. Therefore, the correct radius is approximately 1.65 units, not 5.47 as Jessica calculated.

Her mistake seems to be a misinterpretation of the rearranged formula. The radius of the cylinder is significantly smaller than her calculated value.