Question

Volume of a cylinder is 2,376 cm . If the diameter of its base is 12 cm, then find
its height.

Answer 1

Given :

• Volume of a cylinder is 2,376 cm . If the diameter of its base is 12 cm.

To Find :

• Height of the cylinder.

Solution :

• In the question Volume and diameter of the cylinder is given. so firstly we will Find the Radius Half of diameter is Raduis.

• Then, Using Formula of Volume of Cylinder we will easily find the height .

✰ Volume = 2376cm

✰ Diameter = 12cm

✰ Radius = 12/2 = 6cm

_______________

Volume = πr²h

➤ 2376 = 22/7 × 6 × 6 × H

➤ 2376 = 22/7 × 36 × H

➤ H = 2376/36 × 7/22

➤ H = 21 cm

_______________

Verification :

Volume = πr²h

➤ 22/7 × 6 × 6 × 21

➤ 22/7 × 756

➤ 2376 cm

∴ Height of cylinder is 21cm

_______________

Answer 2

Answer:

• The height of the cylinder is 21 cm.

Step-by-step explanation:

Given :-

• Volume of a cylinder = 2376 cm.
• Diameter of it's base = 12 cm.

To Find :-

• Height of the cylinder.

Basic Terms :-

• Volume : Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object. 
• Diameter : The diameter is the length of the line through the center that touches two points on the edge of the circle.
• Radius : A line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Formula Used :

➊ To find the radius we know that,

✦ Radius = Diameter/2 ✦

where,

• Diameter = 12 cm.

➋ To find the height we know that,

✪ Volume of cylinder = πr²h ✪

where,

• π = 22/7.
• r = radius.
• h = height.

Solution :-

➊ To find the height of the cylinder it is important to have it's radius. Then firstly we will find out the radius of the cylinder.

Given :

• Diameter = 12 cm.

According to the question by using the formula we get,

↦ Radius = Diameter/2

↦ Radius = 12/2

➦ Radius = 6 cm

∴ Hence, the radius of the cylinder is 6 cm.

➋ Now we have the radius of the cylinder. So, now we will find out the height of the cylinder.

Given :

• Volume = 2376 cm.
• π = 22/7.
• r = radius.
• h = height.

According to the question by using the formula we get,

↦ Volume of cylinder = πr²h

↦ 2376 = 22/7 × (6)² × h

↦ 2376 = 22/7 × 6 × 6 × h

↦ 2376 = 22/7 × 36 × h

↦ 2376 × 7 = 22 × 36 × h

↦ 16632 = 792h

↦ h = 16632/792

➦ h = 21 cm

∴ Hence, height of the cylinder is 21 cm.

⦾ Verification ⦾

↦ 22/7 × (6)² × h = 2376

Putting h = 21 we get,

↦ 22/7 × (6)² × 21 = 2376

↦ 22/7 × 6 × 6 × 21 = 2376

↦ 22/7 × 36 × 21 = 2376

↦ 22/7 × 756 = 2376

↦ 2376 = 2376

➦ LHS = RHS

∴ Hence, Verified ✔