Question

The total surface area and curved surface area of a cylinder are in the ratio 5:3 find the ratio between its height and diameter

Answer 1

tsa:csa=5:3

2πr(r+h)/2πrh=5/3
r+h/h=5/3
3r+3h=5h
3r=2h
3(1/2)d=2h
3/2d=2h
3/2*2=h/d
3/1=h/d
hence h:d=3:1

Answer 2

Answer:

3:4

Step-by-step explanation:

tsa:csa = 5:3

2$\pi$r(h+r)/2$\pi$rh=5:3

2$\pi$r will cancel out

(h+r)/r=5:3

cross multiply

3(h+r)=5r

3h+3r=5r

transpose 3h to other side

3r=5h-3h

3r=2h    .....(i)

now r=2d

so d=1/2 r ....(ii)

in eq (i)

3(1/2)d=2h       ...... from (ii)

3/2 d = 2h

2 will get multiplied with 2h

3d=2*2h

3d=4h

transposing 4 and d

3/4=h/d

h:d=3:4

hope it hepls