Question

A test tube shown in fig. has a diameter $20$ mm and height is $15$ cm. The lower portion is a hemisphere. Find the capacity of the test tube. $(\pi =3.14)$

• A. $26.05c{m}^3$
• B. $46.05c{m}^3$
• C. $16.05c{m}^3$
• D. $36.05c{m}^3$

Answer 1

The correct option is B $46.05c{m}^3$

$\Rightarrow$ Radius of test tube $\left(r\right)=\frac{20}{2}=10mm=1cm$

$\Rightarrow$ Height of test tube $=15cm$

Upper portion of test tube is cylinder and lower portion of test tube is hemisphere.

$\Rightarrow$ Height of cylinder $\left(H\right)=h-r=15-1=14cm$

$\Rightarrow$ Volume of test tube $=$ Volume of cylinder $+$ Volume of hemisphere.

$=\pi r^{2}H+\frac{2}{3}\pi r^3$

$=\left(3.14\right)\left(1{)}^2\right(14)+\frac{2}{3}(3.14\left)\right(1{)}^3$

$=43.96+2.09$

$=46.05c{m}^3$

$\Rightarrow$ Capacity of test tube is $46.05c{m}^3$.