Find the radius of the right cylinder shown in which the hei

Find the radius of the right cylinder shown, in which the height of cylinder is equal to its diameter. The lateral area of the right regular triangular prism is 18 cm^2. Find the total surface area. Give your answer in decimal form rounded to 2 decimal places.

Solution

The surface area is 150pi in^2
Total area is 2*pi*r*h + 2*pi*r^2

= 2*pi*r^2 + 2*pi*r*h = 150*pi

= 2*pi*r^2 + 2*pi*r*2r = 150*pi

= 5r^2

= 150

Hence, r = sqrt(30) = 5.48cm