Question

A drinking glass is in the shape of a frustum of a cone of height $14cm$. The diameters of its two circular ends are $4cm$ and $2cm$. Find the capacity of the glass.

• A. $102.67sq.cm$
• B. $92.67sq.cm$
• C. $115.21sq.cm$
• D. $80.21sq.cm$

Answer 1

Answer: (A)

$102.67sq.cm$

Since glass is in the form of frustum, therefore,

$h=14cm,r_1=\frac{4}{2}=2cm$ and $r_2=\frac{2}{2}=1cm.$

$\therefore$ Capacity of frustum $=$ Volume of a frustum

$=\frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)=\frac{1}{3}\times \frac{22}{7}\times 14(2^2+1^2+2\times 1)$

$=\frac{44}{3}(4+1+2)=\frac{44\times 7}{3}=\frac{308}{3}=102.67$ sq. cm.