Question

The sum of the height and radius of the solid cylinder is 37m.If the total surface area of the cylinder be1628msq,find it's volume

Answer 1

ANSWER :

Volume of the cylinder is 4620 m³.

EXPLANATION :

GIVEN :-

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

TO FIND :

• Volume of cylinder.

SOLUTION :

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

Sum of height and radius= 37 m.

Total surface area = 1628 m².

We know,

TSA of cylinder = 2πr(h+r)

According to the question,

$\sf{h+r=37............(i)}$

$\sf{2\pi\:r(h+r)=1628............(ii)}$

✪Taking eq(ii)✪

$\sf{2\pi\:r(h+r)=1628}$

$\implies{2\times\frac{22}{7}\times\:r\times\:37=1628\:\:[From\:eq(i)\:h+r=37]}$

$\implies\sf{r=1628\times\:\frac{1}{2}\times\:\frac{7}{22}\times\:\frac{1}{37}}$

$\implies\sf{r=7}$

† Putting r = 7 in eq .(i) †

h +r = 37

→h + 7 = 37

→h = 37 - 7

→ h = 30

Radius = 7 m.

Height = 30 m.

We know,

Volume of cylinder= πr²h

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

$\implies\sf{Volume\: of\: cylinder=\frac{22}{7}\times\:7\times\:7\times\:30\:m^3}$

$\implies\sf{Volume\:of\: cylinder=4620\:m^3}$

Therefore, volume of the cylinder is 4620 m³.

____________________

Answer 2

AnsWer :

Volume of Cylinder is 4620 m³.

Given :

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

Solution :

• Let height of Cylinder be h m.
• And radius of Cylinder be r m

Given,

$\dashrightarrow\tt h + r = 37 \: m. - - - (1)$

And,

T.S.A of Cylinder

$\dashrightarrow\tt2 \pi r(h + r) = 1628. - - - (2)$

$\rule{200}3$

Taking Equation 2, We get

$\implies\tt2 \pi r(h + r) = 1628.$

By equation 1,

$\implies \tt2 \pi r(37) = 1628.$

$\implies \tt r = \frac{\cancel{1628} \times 7}{2 \times \cancel{37 }\times 22}$

$\implies \tt r = \frac{44 \times 7}{2 \times 22}$

$\implies \tt r = \frac{ \cancel{44} \times 7}{2 \times \cancel{ 22}}$

$\implies \tt r = \frac{ \cancel2 \times 7}{ \cancel2 }$

$\implies \tt r = 7 \: m.$

Now,

Putting the value r in equation (1), We get.

$\implies \tt h + r = 37.$

$\implies \tt h + 7 = 37.$

$\implies \tt h = 30 \: m.$

According to Question,

*Volume of Cylinder = πr²h.

$\implies \tt \pi { r }^{2} h = \frac{22}{\cancel7} \times \cancel7 \times 7 \times 30.$

$\implies \tt \pi { r }^{2} h = 22\times 7 \times 30.$

$\implies \tt \pi { r }^{2} h = 4620 \: {m}^{3} .$

Therefore, the Volume of Cylinder is 4620 m³.