Question

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 cm². Find the volume of the cylinder.

Answer 1

Answer:

The volume of cylindrical solid is 4615.8 cubic meter  

Step-by-step explanation:

Given as :

For cylinder

sum of radius and height = 37 meters

Total surface area of cylinder = 1628 sq cm

Let The radius of cylinder = r meter

Let The height of cylinder = h meters

Let The volume of cylinder = v cubic m

According to question

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

2 π r ( h + r ) = 1628 sq cm

Or, 2 × 3.14 × r ( h + r ) = 1628                .........1

Again

sum of radius and height = 37 meters

r + h = 37                                                .........2

from eq 1 and eq 2

2 × 3.14 × r ( h + r ) = 1628

Or, 2 × 3.14 × r ( 37 ) = 1628

Or, r = $\dfrac{1628}{232.36}$

∴    radius = 7 meters

So, The radius of cylinder = r = 7 meters

put the value of r in e 2

r + h = 37

i.e h = 37 - r

Or,  h = 37 - 7

∴    height = 30 meters

So, The height of cylinder = h = 30 meters

Again

volume of cylinder = π × r² × h

v = 3.14 × (7 m)² × 30 m

volume = 4615.8  cubic meter

So, The volume of cylindrical solid = v = 4615.8 cubic meter

Hence, The volume of cylindrical solid is 4615.8 cubic meter  Answer