Question

a solid right circular cylinder is 15.5 centimeters high and contains 110.0 cubic centimeters of material. compute the cross - sectional area of the cylinder.

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a right circular cylinder is given by the formula \( V = A \times h \), where \( A \) is the cross - sectional area (the area of the circular base) and \( h \) is the height of the cylinder.

Step2: Rearrange the formula to solve for the cross - sectional area

We want to find \( A \), so we can rearrange the formula \( V=A\times h \) to \( A=\frac{V}{h} \).

Step3: Substitute the given values into the formula

We are given that \( V = 110.0\space cm^{3} \) and \( h=15.5\space cm \). Substituting these values into the formula \( A = \frac{V}{h} \), we get \( A=\frac{110.0}{15.5} \).

Step4: Calculate the value of \( A \)

\( \frac{110.0}{15.5}\approx7.10\space cm^{2} \) (rounded to two decimal places).

Answer:

\( 7.10\space cm^{2} \) (corresponding to the option "7.10 sq cm")