Question

The sum of the radius of the base and the height of a solid cylinder is 37 m. If the total surface
area of the cylinder is 1628 m², find its volume​

Answer 1

Answer:

The volume of cylinder = 4620m³

Answer 2

Answer:

The volume of the cylinder is 4620 m³.

Step-by-step-explanation:

We have given that,

The sum of the radius of base and height of a cylinder is 37 m.

The total surface area of the cylinder is 1628 m².

We have to find the volume of the cylinder.

Now,

r + h = 37 - - ( 1 ) [ Given ]

Now, we know that,

Total surface area of cylinder = 2 π r ( r + h )

⇒ 1628 = 2 * 22 / 7 * r * ( 37 ) - - [ From ( 1 ) ]

⇒ 1628 = 2 * 22 / 7 * r * 37

⇒ ( 1628 * 7 ) / ( 2 * 22 * 37 ) = r

⇒ r = ( 1628 * 7 ) / ( 2 * 22 * 37 )

⇒ r = 1628 ÷ 37 * 7 / 44

⇒ r = 44 * 7 / 44

⇒ r = 44 ÷ 44 * 7

⇒ r = 1 * 7

⇒ r = 7 m

Now, by substituting r = 7 in equation ( 1 ), we get,

r + h = 37 - - ( 1 )

⇒ 7 + h = 37

⇒ h = 37 - 7

⇒ h = 30 m

Now, we know that,

Volume of cylinder = π r² h

⇒ Volume of cylinder = 22 / 7 * 7² * 30

⇒ Volume of cylinder = 22 / 7 * 7 * 7 * 30

⇒ Volume of cylinder = 22 * 7 ÷ 7 * 7 * 30

⇒ Volume of cylinder = 22 * 1 * 7 * 30

⇒ Volume of cylinder = 22 * 7 * 30

⇒ Volume of cylinder = 22 * 210

⇒ Volume of cylinder = 4620 m³

∴ The volume of the cylinder is 4620 m³.