Question

Total surface area of solid right circular cylinder is 1540cm square .if its height is 4 times the radius of the base then find the height of the cylinder.

Answer 1

Hello.......... ^_^

Here is your answer,

Given :-total surface area of right circular cylinder is 1540cm square.

(according to the question)
The height of the cylinder is 4 times of the radius of the base.

Let radius be 'r' cm
so, height = 4 times of radius = 4r cm

$Total \: \: surface \: \: area \: = 2\pi \: r(r + h) \\ \\ = > 1540 = 2 \times \frac{22}{7} \times r(r + 4r) \\ \\ = > 1540 = \frac{44}{7} \times r( r+4r ) \\ \\ = > 1540 \div \frac{44}{7} = r(r + 4r) \\ \\ = > 1540 \times \frac{7}{44} = r \times 5r \\ \\ (1540 \div 44 = 35) \\ \\ = > 35 \times 7 = 5 {r}^{2} \\ \\ = > 245 = {5r}^{2} \\ \\ = > \frac{245}{5} = {r}^{2} \\ \\ (245 \div 5 = 49) \\ \\ = > 49 = {r}^{2} \\ \\ = > \sqrt{49} = r \\ \\ = > 7 = r$
so,
radius = r = 7cm
and height = 4 r = 4 X 7 = 28cm


Hope it helps............ ^_^