Question

In a solid cylinder,sum of height and radius of the base is equal to 37 cm.Total surface area of the cylinder is 1628cm².What is the volume of cylinder in cubic cm?

Answer 1

In the above Question , the following information is given -

In a solid cylinder, the sum of height and radius of the base is equal to 37 cm.

The Total surface area of the cylinder is 1628 cm² .

To find -

What is the volume of cylinder in cubic cm ?

Solution -

Here ,

The sum of height and radius of the base is equal to 37 cm.

Let us Assume that the height of the cylinder is h cm and the radius of the base is r cm .

Now ,

h + r = 37 .......... { 1 }

Now , we know that &

Total Surface area of a Cylinder -

=> 2 π r ( h + r ) .

But , ( h + r ) = 37

=> 2 π r ( 37 )

=> 74 π r .

So , the total surface area of the cylinder -

=> 74 π r .

But , it is 1628 cm²

So ,

=> 74 π r = 1628

=> π r = 22

=> r = 7 cm .

But , ( h + r ) = 37

So, h = 30 cm .

Thus , we can conclude that the radius and height of the given cylinder are 7 cm and 30 cm respectively.

Now ,

Volume Of the Cylinder -

=> π r² h

=> ( 22 / 7 ) × 7 ² × 30 .

=> 22 × 7 × 30

=> 4620 cm ³ .

Thus , the required volume is 4620 cm³.

_______________________________________________

Answer 2

⋆ Given ⋆

• In a solid cylinder, sum of height and radius of the base is equal to 37 cm.
• Total surface area of the cylinder is 1628 cm².

⋆ To Find ⋆

The volume of cylinder in cubic cm.

⋆ Solution ⋆

Let the height of the cylinder be h and the radius be r.

A/q,

r + h = 37 cm           ... (i)

We know for a cylinder,

• TSA = 2πr(r + h)

⇒ 1628 = 2πr(37)

⇒ 1628 = 74πr

⇒ πr = 1628/74

⇒ πr = 22

Taking π as 22/7,

⇒ 22/7 × r = 22

⇒ r/7 = 1

⇒ r = 7 cm

Putting the value of r in eq. (i) :

r + h = 37

→ h = 37 - r

→ h = 37 - 7

→ h = 30 cm

_______________________

Volume of a cylinder = πr²h

⇒ Volume = 22/7 × (7)² × 30

⇒ Volume = 22/7 × 7 × 7 × 30

⇒ Volume = 22 × 7 × 30

⇒ Volume = 4620 cm³

Hence, the volume of the cylinder is 4620 cm³.