Question

The given table shows the color and radius of balls placed in a bag.

Color of ball	Radius of ball(in cm)
Red	$4$
Blue	$5$
Yellow	$3$

Which ball has the maximum volume?

• A. Red
• B. Blue
• C. Yellow
• D. All have equal volume

Answer 1

The correct option is B Blue

Radius of red ball $\left(r_1\right)=4cm$

Volume of red ball $=\frac{4}{3}\pi r_1^3$
$=\frac{4}{3}\pi (4{)}^3$
$=\frac{256}{3}\pi c{m}^3$

Radius of blue ball $\left(r_2\right)=5cm$

Volume of blue ball $=\frac{4}{3}\pi r_2^3$
$=\frac{4}{3}\pi (5{)}^3$
$=\frac{500}{3}\pi c{m}^3$

Radius of yellow ball $\left(r_3\right)=3cm$


Volume of red ball $=\frac{4}{3}\pi r_3^3$
$=\frac{4}{3}\pi (3{)}^3$
$=\frac{108}{3}\pi c{m}^3$

As the denominators are same we can compare the numerators directly.
Hence,
$\frac{108}{3}\pi c{m}^3<\frac{256}{3}\pi c{m}^3<\frac{500}{3}\pi c{m}^3$

Blue ball has the maximum volume.

Therefore, option (b.) is the correct answer.