Question

. 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 the total surface area of the toy.es I​

Answer 1

Right circular cone

Solve for surface area

A≈213.21cm²

r Radius

3.5

cm

h Height

15.5

cm

Using the formulas

A=πrl+πr2

l=r2+h2

Solving forA

A=πr(r+h2+r2)=π·3.5·(3.5+15.52+3.52)≈213.20692cm²

Answer 2

Answer:

214.5 cm² is the correct answer.

Step-by-step explanation:

Given,

• Common Radius of the toy = 3.5 cm
• Total Height of the toy        = 15.5 cm
• ∴ Height of the cone           = 15.5 - 3.5 = 12 cm

Total Surface Area of the toy = Curved Surface Area of Cone + Curved                                Surface Area of Hemisphere

                                                = (π × r × l) + (2 × π × r²)

                                                = π × r × (l + 2r)

In the Cone, we have Base and Height. So we can calculate the Slant Height of the cone by using Pythagorean Formula.

⇒ (l)² = (b)² + (h)²

⇒ l    = √(12.25 + 144)

        = √156.25

        = 12.5 cm

⇒ π × r × (l + 2r)

⇒ 22/7 × 3.5 × (12.5 + 7)

⇒ 22 × 0.5 × 19.5

⇒ 214.5 cm²               ←ANSWER  

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