Question

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

Answer 1

Answer :-

We know that ,

Sum of height and radius of cylinder = 37m

i.e, (h + r = 37m)

Total surface area = 1628m

Formula of TSA of cylinder = 2πr (r+h)

TSA of cylinder = 2πr (37) = 1628m

2πr = 44m

πr = 22m

r = 7m

So, (r + h) = 37m

h = (37 - 7) = 30m

Volume of cylinder $=\pi {r}^{2} h$

$=\frac{22}{7} \times 7 \times 7\times 30$

$= 22 \times 7 \times30$

$= 462 {m}^{2}$

$\bold{Volume=462{m}^{2}}$

Answer 2

Total length of the cylinder (h + r ) = 37m

Total surface area of the cylinder = 1628 m

Formula to find the TSA of cylinder = 2π r( r+ h)

TSA = 2πr (37)

1628 = 2πr (37)

$\frac{1628}{37}$= 2πr

2πr = 44

πr = $\frac{44}{2}$

πr = 22

r = $\frac{22 × 1}{7 × 22}$

r = 7m

We already know that (r + h) = 37m

(7+h) = 37m

h = (37 - 7)

h = 30m

Volume of cylinder =$\pi {r}^{2}$ h

=$\frac{22}{7} \times 7 \times 7\times$ 30

= $22 \times 7 \times30$

= 462 {m}^{2}

So the volume of the cylinder is 462 ${m}^{2}$