Question

Diameter of cylinder A is 6 cm, and the height is 15 cm. Diameter of cylinder B is 15 cm and height is 6 cm. Find the cylinder which has the greatest volume.

Answer 1

Answer:

Volume of Cylinder B is greater than volume of Cylinder A .

Step-by-step explanation:

We Have :-

Cylinder A :-

Diameter = 6 cm

Height = 15 cm

Cylinder B :-

Diameter = 15 cm

Height = 6 cm

To Find :-

Which cylinder has more volume

Formula Used :-

$volume \: of \: cylinder \: = \: \pi \: {r}^{2} \: h$

Solution :-

Volume of Cylinder A :-

$volume \: of \: cylinder \: = \: \pi \: {r}^{2} \: h \\ \\ volume \: of \: cylinder \: = \: \dfrac{22}{7} \times \: {3}^{2} \times \: 15 \\ \\ volume \: = \: \dfrac{2970}{7} \\ \\ volume \: = \: 424.29 \: {cm}^{3}$

Volume Of Cylinder B :-

$volume \: of \: cylinder \: = \: \pi \: {r}^{2} \: h \\ \\ volume \: of \: cylinder \: = \: \dfrac{22}{7} \times \: {7.5}^{2} \times \: 6 \\ \\ volume \: = \: \dfrac{7425}{7} \\ \\ volume \: = \: 1060.71 \: {cm}^{3}$

Volume of Cylinder B is greater than volume of Cylinder A .

Answer 2

Given

• Diameter of cylinder A = 6 cm
• Height of cylinder A = 15 cm
• Diameter of cylinder B = 15 cm
• Height of cylinder B = 6cm

To find

• The cylinder which has the greatest volume

Solution

We have 2 cylinders and we are given with their diameters and heights and asked to find their volumes and compare them.

Cylinder A :-

• Diameter = 6 cm
• Radius = Diameter/2
• Radius = 3 cm
• Height = 15 cm

Volume of cylinder =  πr²h

• 22/7 × 3 × 3 × 15
• 2970 / 7
• 424.29

Hence, the volume of cylinder A = 424.29 cm³

Cylinder B :-

• Diameter = 15 cm
• Radius = Diameter/2
• Radius = 15/2
• Height = 6 cm

Volume of cylinder =  πr²h

• 22/7 × 15/2 × 15/2 × 6
• 7425/7
• 1060.71

Hence, the volume of cylinder B is 1060.71 cm³

Now, on comparing the both volumes,

Volume of cylinder B is greater than volume of cylinder A

• 1060.71 is greater than 424.29

Therefore, Cylinder B has the greatest volume.