Question

The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use π = 3.14] 

Answer 1

We have,

Height, h = 8 cm

Base radii, R = 18 cm and r = 12 cm

Also, the slant height, `l = sqrt(("R" - r)^2 + "h"^2)`

`=sqrt((18-12)^2+8^2)`

`= sqrt(6^2 + 8^2)`

`= sqrt(36+64)`

`= sqrt(100)`

= 10 cm

Now ,

Total surface area of the solid frustum `= pi ("R" + r)l + pi"R"^2 + pi"r"^2`

= 3.14 × (18 + 12) × 10 + 3.14 × 18² + 3.14 + 12² 

= 3.14  × 30 × 10 + 3.14 ×324×144

= 3.14 × (300 + 3324 + 144)

= 3.14 × 768

= 2411.52 cm² 

So, the total surface area of the solid frustum is 2411.52 cm².