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

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. ("use " pi=22/7)

#### Solution

Let the radius of base and height of the solid right circular cylinder be r cm and h cm, respectively.

According to the question,

r+h=37                 .....(1)

Total surface area=1628 sq cm

2πr(r+h)=1628   .....(2)

From (1) and (2), we get

2πr(37)=1628

2πr=44

=>2xx22/7xxr=44

=>r=(44xx7)/(2xx22)

⇒ 7 cm

Substituting the value of r in (1), we get

7+h=37

⇒ 30 cm

Now,

Volume of the cylinder = πr2h

=22/7xx7xx7xx30

=4,620 cm3

Hence, the volume of the cylinder is 4,620 cm3.

Concept: Surface Area of a Combination of Solids
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 56 | Page 31