Question

find the surface area of each figure. complete parts (a) through (e) below
the surface area of the right regular prism is 232 cm²
(simplify your answer. type an exact icals as needed. type an exact answer, using π as needed.)
d. sphere
the surface area of the sphere is □
(simplify your answer. type an exact answe using radicals as needed. type an exact answer, using π as needed)

Explanation:

Step1: Recall the formula for the surface area of a sphere

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\), where \(r\) is the radius of the sphere.

Step2: Identify the radius of the sphere

Given that the diameter \(d = 7\space cm\), and the radius \(r=\frac{d}{2}\), so \(r=\frac{7}{2}\space cm\)

Step3: Substitute the radius into the formula

Substitute \(r = \frac{7}{2}\) into \(S = 4\pi r^{2}\). We get \(S=4\pi(\frac{7}{2})^{2}\)
First, calculate \((\frac{7}{2})^{2}=\frac{49}{4}\)
Then \(S = 4\pi\times\frac{49}{4}\)
The \(4\) in the numerator and denominator cancels out.

Answer:

\(49\pi\space cm^{2}\)