a toy is in the form of cone of radius 3.5 CM mounted on a hemisphere of same radius .the total height of the toy is 15.5 cm find the total surface area of the toy
Answers
Solution:
Given:
➜ A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm.
Find:
➜ Find the total surface area of the toy.
According to the given question:
➜ 3.5 cm = radius of the cone and the hemisphere.
➜ 15.5 cm = total height of the toy.
➜ 12 cm = height of the cone = (3.5 - 15.5 = 12cm).
Calculations:
➜ Slant height of cone (I) = √h² + r²
➜ I = √12² + (3.5)²
➜ I = √12² + (7/2)²
➜ I = √144 + 49/4 = √(576 + 49)/4 = √625/4
➜ I = 25/2
Formulas:
- πrl is curved surface area of cone.
- 2πr2 is the curved surface area of the hemisphere.
➜ (22/7 × 7/2 × 25/2) = 275/2 cm²
➜ 2 × 22/7 × (7/2)
➜ 2 77 cm²
Formula:
Total surface area of toy = Curved Surface Area of cone + Curved Surface Area of hemisphere.
➜ (275/2 + 77) cm²
➜ (275 + 154)/2 cm²
➜ 429/2 cm²
➜ 214.5 cm²
Therefore, 214.5 cm² is the total surface area of the toy.