Question

the sum of the radius and height of a cylinder is 37 cm and the total surface area of the cylinder is 1628sq. cm. find the height of cylinder​

Answer 1

Step-by-step explanation:

total surface area of cylinder = 2×pie ×r×(r +h)

1628 =2×pie×r×(r+h)

1628=2×22/7×r×(r+h)

1628=44/7×r×37

1628×7=44×37×r

11396=1628×r

11396/1628=r

7 cm=r

radius =7cm

sum of radius +height =37cm

7cm +h=37

h=37 minus 7

h=30cm

height =30cm

Answer 2

Given that:

• The sum of the radius and height of a cylinder is 37 cm.
• The total surface area of the cylinder is 1628 sq. cm.

To Find:

• The height of cylinder.

Formula used:

• TSA = 2πr(r + h)

Here,

• TSA = Total surface area of a cylinder
• r = Radius of a cylinder
• h = Height of a cylinder

Finding the radius of cylinder:

ㅤ↠ㅤ1628 = 2π × r × 37

ㅤ↠ㅤ1628 = 74πr

ㅤ↠ㅤ74 × 22 = 74 × πr

Cancelling 74 both sides.

ㅤ↠ㅤ22 = πr

ㅤ↠ㅤ22 = 22r/7

Canveling 22 both sides.

ㅤ↠ㅤ1 = r/7

ㅤ↠ㅤr = 7

Now finding the height of the cylinder:

ㅤ↠ㅤr + h = 37

ㅤ↠ㅤ7 + h = 37

ㅤ↠ㅤh = 37 - 7

ㅤ↠ㅤh = 30

Hence,

• The height of the cylinder is 30 cm.