Question

The sum of the radius and the height of a solid cylinder is 37 cm If the total surface area of the solid is 1628 cm${}^2$ find the circumference of the base and the volume of the solid

• A. 44 cm, 4620 cm${}^3$
• B. 44 cm, 4610 cm${}^3$
• C. 33 cm, 4620 cm${}^3$
• D. 44 cm, 4600 cm${}^3$

Answer 1

The correct option is A 44 cm, 4620 cm${}^3$

Given r+h=37 cm
Total surface area of the solid cylinder = 2$\pi r(r+h)=1628c{m}^2$
$\therefore r=\frac{1628\times 7}{2\times 22\times 37}=7cm$
$\therefore$ Height = (37-7) cn = 30 cm
and Circumference = $2\pi r=\frac{22}{7}\times 7=44cm$
Volume of the cylinder = $\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 30=4620c{m}^3$