Question

the ration between the curved surface and total surface of a culinder is 1:2 find the volume of the cylinder given that is total surface area us 616cm2

Answer 1

CSA/TSA=1/2
2πrh/2πr(h+r)=1/2
4πrh=2πrh+2πr²
2πrh=2πr²
h=r
TSA=616
2πrh+2πr²=616
4πr²=616
r²=49
r=7cm
h=7cm
Volume of cylinder=πr²h
=(22/7)*7*7*7
=1078cm³

Answer 2

We know that curved surface area of the cylinder = 2pirh  ----- (1)

We know that Total surface area of the cylinder = 2pir(r + h)  ----- (2)

Given that the ratio between the curved surface area and the total surface area of the cylinder = 1:2.

$\frac{2 \pi rh}{2 \pi r(r + h)} = \frac{1}{2}$

$\frac{h}{h + r} = \frac{1}{2}$

On cross-multiplication, we get

2h = h + r

2h - h = r

h = r   -------- (3).


Given that total surface area of the cylinder = 616cm^2.  ------ (4)

Substitute (4) in (2), we get

616 = 2pir(r + h)

616 = 2 * 22/7 * r(r + r)

616 = 2 * 22/7 * r(2r)

616 = 2 * 22/7 * 2r^2

616 * 7 = 2 * 22 * 2r^2

4312 = 44 * 2r2

98 = 2r^2

98/2 = r^2

49 = r^2

7 = r. 

Therefore from (3),

we get h = r =  7cm.

We know that volume of a cylinder = $\pi r^{2} h$

                                                            = $\frac{22}{7} * 7^{2} * 7$

                                                            = 22 * 49

                                                            = 1078cm^3.



Hope this helps!