Find the ratio of the curved surface area to the total surface area of a cylinder with diameter of base 14 cm and height 10 cm.
- A17
10
- B17
5
- C17
13
- D17
11
Solution & Step-by-step Explanation
Given parameters:
Diameter of base = 14 cm⟹Radius (r)=
2
14
=7 cm
Height of cylinder (h)=10 cm
The formulas for surface areas are:
Curved Surface Area (CSA)=2πrh
Total Surface Area (TSA)=2πr(h+r)
The required ratio is:
Ratio=
TSA
CSA
=
2πr(h+r)
2πrh
=
h+r
h
Substituting the values of h and r:
Ratio=
10+7
10
=
17
10
Diameter of base = 14 cm⟹Radius (r)=
2
14
=7 cm
Height of cylinder (h)=10 cm
The formulas for surface areas are:
Curved Surface Area (CSA)=2πrh
Total Surface Area (TSA)=2πr(h+r)
The required ratio is:
Ratio=
TSA
CSA
=
2πr(h+r)
2πrh
=
h+r
h
Substituting the values of h and r:
Ratio=
10+7
10
=
17
10