Question

A circle is circumscribed around a rectangle with sides lengths 6 and 8 what is the area of the circle?

A. 16
`\pi`
B. 20
`\pi`
C. 24
`\pi`
D. 25
`\pi`
E. 30
`\pi`

Answer 1

D. 25pi

Explanation:

"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)

6^2 + 8^2 = d^2

36 + 64 = d^2

100 = d^2

d = 10

This is the diameter of the circle. The radius would then be 5.

Area of a circle is:

A = pi•r^2

= pi•5^2

= 25pi