Question

the radii of the circular ends of a solid frustum of a cone are 18cm and 12cm and its height is 8cm .Find its total surface area .

Answer 1

Answer: 2411.52 cm²

Step-by-step explanation:

We have , Height = 8 cm

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

Also, the slant height  

l = √(R -r)² + h²

 = √(18-12 )² + 8²

   = √ 6² +8²

  = √36 + 64

  = √100

 = 10 cm

Now ,

Total surface area of the solid frustum

π(R+r)l +πR² +πr²

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

= 3.14 × ( 300 + 324 + 144 )

3.14 × 768

= 2411.52 cm²

So the total surface area of the frustum is 2411.52 cm²

Answer 2

Answer:

2413.72 cm²

Step-by-step explanation:

Find slated height:

Slanted height = √(h² + (R - r)²)

Slanted height = √(8² + (18 - 12)²)

Slanted height = √100

Slanted height = 10 cm

Find the total surface area:

TSA = π(R + r)l + πR² + πr²

TSA = ( π(18 + 12) x 10 ) + π18² + π12²

TSA = 300π + 324π + 144π

TSA = 768π = 2413.72 cm² (Taking π as 22/7)

Answer: The total surface area is 2413.72 cm²