Question

The diameter of a sphere is 3.34m. Calculate its volume with due regard to significant figures.

Answer 1

Hint: Volume of a sphere is ${\displaystyle \frac{4}{3}}\pi {\left(r\right)}^3$. The term in the formula is a radius, not diameter. Use the relation of the radius with diameter. Value of π is 3.14. A significant figure is nothing but rounding off the value we get after calculation.

Complete step by step solution:
In this question, we need to find out what is the volume of a sphere having diameter 3.34m with due regard to significant figures.

Note that in question we have given diameter, not radius. So convert diameter into radius by diving diameter by 2.

Radius = diameter/2

$$Radius=\left({\displaystyle \frac{3.34}{2}}\right)$$

We know that volume of a sphere is given by,

$volume(V)={\displaystyle \frac{4}{3}}\pi {\left(r\right)}^3={\displaystyle \frac{4}{3}}\pi {\left({\displaystyle \frac{3.34}{2}}\right)}^3=19.5169m^3$

Round off the value of volume. We get,

$V=19.5m^3$

The volume of the sphere is$V=19.5m^3$.

Since we can round off up to one digit. If the second digit after a point is greater than 4 then 19.5 will be converted into 19.6.

Note: Above question is very straight forward. We just need to find out the volume. But focus on the container. Here the container is a sphere, not cone or cylinder. So use an appropriate formula of volume of a sphere. Keep the formula of the sphere in mind by memorising the key number which is 4/3.