Question

the pythagorean theorem can be used to calculate: a. the surface area of a sphere b. the area of a circle c. the length of the diagonal in a rectangle d. the volume of a cylinder

Explanation:

Step1: Recall Pythagorean Theorem

$$a^{2}+b^{2}=c^{2}$$

Step2: Analyze each option

• Option a: Surface area of sphere formula is $4\pi r^{2}$, no relation to Pythagorean Theorem.
• Option b: Area of circle formula is $\pi r^{2}$, no relation to Pythagorean Theorem.
• Option c: In a rectangle with sides \(a\) and \(b\) and diagonal \(c\), by Pythagorean Theorem \(c = \sqrt{a^{2}+b^{2}}\).
• Option d: Volume of cylinder formula is $\pi r^{2}h$, no relation to Pythagorean Theorem.

Answer:

C. The length of the diagonal in a rectangle