Question

A wooden toy is in the shape of a cone mounted on a cylinder. The height of cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone is 10 cm. If the radius of base of the cylinder is half of the radius of the base of the cone, find the total surface area of the toy. (Use π = 3.14).

Answer 1

Height of the cone = 24 cm

Height of the cylinder = h₂​ = 60 − 24 = 36 cm

Radius of the cone = twice the radius of the cylinder = 10 cm

Total height of toy = 60 cm

Step 1: Find slant height of cone

Slant height of the cone = `sqrt(r^2 + h^2)` 

= `sqrt(10^2 + 24^2)` 

= `sqrt(100 + 576)` 

= `sqrt(676)` 

= 26 cm 

Step 2: Curved surface area of a cone

`CSA_"cone​" = πRl`

= 3.14 × 10 × 26

= 816.4 cm²

Step 3: Curved surface area of a cylinder

`CSA_"cyl" ​=2πrh_2`

= 2 × 3.14 × 5 × 36

= 1130.4 cm²

Step 4: Exposed plane area (= πR²)     ...[= ring under cone + bottom of cylinder together]

πr² = 3.14 × 102

= 3.14 × 100 = 314 cm²

Step 5: Total surface area

TSA = 816.4 + 1130.4 + 314

= 2260.8 cm²