The sum of the base radius and the height of a solid right circular solid cylinder is 37 cm. If the total surface area of the cylinder is 1628 sq.cm, then find the volume of the cylinder.

GIVEN : radius of cylinder be “r” and its height be “h”

r + h = 37cm

TSA (total surface area) of the cylinder = 1628 sq.cm

we take π =

TO FIND : volume of a solid cylinder = ?

PROCEDURE :

As we know that, TSA of a cylinder = 2π r(r + h)

Now putting the values of “r + h” and “TSA” in the above formula,

We get,

1628 = 2π r(37)

= 2π r

44 = 2π r

r = = = = 44 × = 7cm

∴ r = 7cm

Now we have, r + h = 37

So, we have, 7 + h = 37

So, h = 37-7 = 30cm

∴ h = 30cm

Now that we have values of radius and height of the cylinder, we can find the volume of the cylinder.

Volume of the cylinder “V” = π r²h

V = π ×(7)²×(30)

= × 7 × 7 × 30

= 22 × 7 × 30

= 4620 cm³

∴ The volume of the given cylinder is 4620 cm³.