Question

A solid toy is in the form of a right circular with hemispherical ends. The total height of the solid is 19 cm and diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid. (Take $\pi =\frac{22}{7}$)

• A. Volume = $681.66c{m}^3;$ Total Surface Area = $478c{m}^2$
• B. Volume = $681.66c{m}^3;$ Total Surface Area = $418c{m}^2$
• C. Volume = $641.66c{m}^3;$ Total Surface Area = $478c{m}^2$
• D. Volume = $641.66c{m}^3;$ Total Surface Area = $418c{m}^2$

Answer 1

Answer: (D)

Volume = $641.66c{m}^3;$ Total Surface Area = $418c{m}^2$

height of the solid = 19 cm,
and diameter of the cylinder = 7 cm, radius=3.5 cm,
Height of the cylinder =19-7=12 cm,
the volume of the solid=volume of cylinder+volume of 2 hemisphere
$V=\Pi r^{2}h+2\ast \Pi \frac{2}{3}{r}^3$
$V=\frac{22}{7}{\times 3.5}^2\times 12+2\ast \frac{22}{7}\times \frac{2}{3}{3.5}^3$
$V=\frac{22}{7}{\times 3.5}^2\times 12+2\ast \frac{22}{7}\times \frac{2}{3}{3.5}^3$
$V=462+179.67$
$V=641.67c{m}^3$
total surface area of the solid=
$S_a=2\times 2\Pi r^2+2\Pi rh$
$S_a=2\times 2\times \frac{22}{7}{3.5}^2+2\frac{22}{7}\times 3.5\times 12$
$S_a=154+264=418$
Answer $641.66c{m}^3;418c{m}^2$