Question

the sum of the radius of the base and height of a solid cylinder is 37 m. if the total surface area of tbe cylinder is 1628 sq. m. find its volume​

Answer 1

Answer:

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Answer 2

Given:-

• Sum of the radius of the base and height of solid is 37m.
• Total surface area of the cylinder is 1628 m².

Find:-

Volume of the cylinder.

$\rule{100}2$

Solution:-

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

We have given that sum of radius (R) and height (H) of solid is 37m.

=> r + h = 37

=> r = 37 - h ....(eq 1)

Also we have given that, total surface area of cylinder is 1628 m².

Formula used here is :-

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

Substitute the known values in above formula

=> 1628 = 2 × 22/7 × r (r + h)

=> 1628 = 2 × 22/7 × (37 - h) (37 - h + h)

[From (eq 1)]

=> 1628 = 44/7 × (37 - h) (37)

=> (1628 × 7)/44 = 37(37 - h)

=> 259 = 37(37 - h)

=> 7 = 37 - h

=> h = 30 m

Therefore,

=> r = 37 - 30

=> r = 7 m

Now, we have to find the volume of cylinder.

Formula used here is :-

Volume of cylinder = πr²h

Substitute the known values

=> 22/7 × 7 × 7 × 30

=> 22 × 7 × 30

=> 4620 m³

$\rule{100}2$ [Answer]