The ratio of the curved surface area of a cylinder to its total surface area is 7:10, respectively. If the volume of the cylinder is 12672 cm³, then find the curved surface area of the cylinder.
Show answer & explanation
Correct answer: C
Explanation
Has been given :
Curved surface area : Total surface area = 7 : 10
Volume of cylinder = 12672 cm³
According to the formula:
CSA = 2πrh
TSA = 2πr(h + r)
CSA / TSA = 7 / 10
2πrh / 2πr(h + r) = 7 / 10
h / (h + r) = 7 / 10
10h = 7h + 7r
3h = 7r
h = 7k, r = 3k
volume
πr²h = 12672
22/7 × (3k)² × 7k = 12672
22/7 × 9k² × 7k = 12672
198k³ = 12672
k³ = 64
k = 4
r = 12 cm
h = 28 cm
CSA= 2πrh
= 2 × 22/7 × 12 × 28 = 2112 cm²