the volume of a cylinder is 12,566.4 cm3. The height of the cylinder is 8 cm.

Question

Find the area of the base of the cylinder to the nearest tenth of a centimeter.

Find the lateral area to the nearest tenth of a centimeter

Find the surface area of the cylinder.

Answer 1

Volume of the cylinder V = A·h, i.e. to find volume you multiply area A of the base by height h.

Hence A = V / h. Or A = 12,566.4 / 8 = 157.05 (cm²); if we round it, will be 157,1 cm². This is a special case, when 157.0 also could be written as an answer.

For a right cylinder the lateral area is the area of the side surface of the cylinder A_L = 2πRh. To find radius of the cylinder, we recall the formula for base area A = πR². from this formula R = √(A / π). After putting the value of area and π = 3.14 and calculations, we get R = √( 157.05 / 3.14 = 7.07 (cm) or 7.1 cm.

Now for lateral area we have A = 2·3.14·7.1·8 = 356.7 cm².

The surface area is a sum of lateral area and 2 sums of base area.

Thus, A = 356.7 cm² + 2 x 157.1 cm² = 670.9 cm².