Question

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m², find the circumference of its base.

 

Answer 1

\[\text{ Let r and h be the radius and height of the solid cylinder }  . \]
\[\text{ Given: }  \]
\[r + h = 37 m\]
\[\text{ Total surface area, } S = 2\pi r\left( r + h \right)\]
\[1628 = 2\pi \times r \times 37\]
\[ r = \frac{1628}{2\pi \times 37}\]
\[ = \frac{1628}{232 . 477}\]
\[ = 7 m\]
\[\text{ Circumference of its base } , S_1 = 2\pi r\]
\[ = \left( 2 \times \frac{22}{7} \times 7 \right) m\]
\[ = 44 m\]