Question

A solid toy is in the form of a right circular cylinder with a hemispherical shape of one end and a cone at the other end. Then common diameter is $4.2cm$ and the heights of the cyndrical and conical portions are $12cm$ and $7cm$, respectively. Find the volume of the solid. (Take $\pi$ = 22/7)

• A. $218.02c{m}^3$
• B. $178.66c{m}^3$
• C. $158.66c{m}^3$
• D. $138.66c{m}^3$

Answer 1

Answer: (A)

$218.02c{m}^3$

Diameter of base of conical part=$4.2cm$

Diameter of base of cylindrical part=$4.2cm$

Diameter of hemispherical part$=4.2m$

Therefore radius$=2.1cm$

Height of conical part, $h_1=7cm$

Height of cylindrical part, $h_2=12cm$

Volume of toy=volume of cone +volume of cylinder+volume of hemisphere

$=\frac{1}{3}\pi r^2{h}_1+\pi r^2{h}_1+\frac{2}{3}\pi r^3$

$=\pi r^2(\frac{h_1}{3}+h_2+\frac{2r}{3})$

$=\frac{22}{7}\times 2.1\times 2.1(\frac{7}{3}+12+\frac{2\times 2.1}{3})$

$=\frac{22}{7}\times 2.1\times 2.1\times 15.73$

$=218.02c{m}^3$