Question

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

Answer 1

Given that, a test tube has a diameter of $20mm$ and height of $15cm$. The lower portion of the test tube is a hemisphere.

To find out: The capacity of the test tube.

We can see that the test tube combines two shapes, a hemispherical bottom and cylindrical body.

Radius of hemisphere $=\frac{20}{2}mm=1cm[\because 1cm=10mm]$
We know that, the volume of a hemisphere $=\frac{2}{3}\pi r^3$

$\therefore$ Volume of the hemispherical bottom of the test tube $=\frac{2}{3}\times 3.14\times (1{)}^3$

$\Rightarrow 2.09c{m}^3$

Now, height of the cylindrical portion $=$ height of the test tube $-$ radius of the hemispherical bottom
$\Rightarrow 15-1=14cm$

We know that volume of a cylinder $=\pi r^{2}h$

$\therefore$ Volume of the cylindrical portion $=3.14\times (1{)}^2\times 14$
$\Rightarrow 43.96c{m}^3$

Capacity of the test tube $=$ Volume of cylindrical portion $+$ Volume of hemispherical portion
$\therefore$ Capacity $=43.96+2.09$
$\Rightarrow 46.05c{m}^3$

Hence, the capacity of the given test tube is $46.05c{m}^3$.