Question

The sum of the height and radius of a cylinder is 9 m. The surface area of the cylinder is 54 pi m^2. Find the height and the radius.

Answer 1

Let h be the height and r be the radius.

r + h = 9 ------ (1)

Surface area of the cylinder = 2(pi)rh + 2(pi)r^2 = 54 ------ (2)

Two equations, two unknowns. Solve for r and h

Answer 2

the whole guess check im assuming

Answer 3

No guessing. Simplify the second equation by dividing throughout by 2pi.
Find r from equation 1 in terms of h, put in (2) and solve for h. Then solve for r.

Answer 4

h=6 r=3

Answer 5

\[SA=2 \pi(3*6)+2\pi(3^2)\]
\[SA=2 \pi (18)+2 \pi (9)\]
\[SA= 2(18\pi)+2(9)\pi\]
\[SA=36\pi+18\pi\]
\[SA=54 \pi m ^2\]