If the height and diameter of a cylinder are 12 cm and 28 cm, respectively, then find the ratio of the total surface area to the curved surface area.

Question

Accepted Answer

Given:  
Height (h) = 12 cm    
Diameter (d) = 28 cm  
Radius (r) = d/2 = 28/2 = 14 cm

Curved Surface Area (CSA) of cylinder = 2 * π * r * h  
= 2 * π * 14 * 12  
= 336π cm²

Total Surface Area (TSA) of cylinder = 2 * π * r * (r + h)  
= 2 * π * 14 * (14 + 12)  
= 2 * π * 14 * 26  
= 728π cm²

Ratio of TSA to CSA = 728π : 336π = 728 : 336
Divide numerator and denominator by 56:  
728 ÷ 56 = 13  
336 ÷ 56 = 6

Ratio = 13 : 6

However, the options given are 13:5, 10:3, 13:6, and 11:6. The correct ratio is 13:6.

Double-checking the calculation:  
CSA = 2πrh = 2 * π * 14 * 12 = 336π  
TSA = 2πr(r + h) = 2 * π * 14 * (14 + 12) = 2 * π * 14 * 26 = 728π  
Ratio TSA : CSA = 728π : 336π = 728 : 336  
Simplify by dividing both by 56:  
728/56 = 13  
336/56 = 6  
  
So the ratio is 13 : 6.

Therefore, the correct answer is option 3: 13 : 6.

Answer

Answer

Answer