Aditi went to a painter to get her two wooden toys painted.
Toy 1 is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. total h of toy is 15.5 cm
Toy 2 is in the form of a hemispherical bowl of diameter 7 cm mounted by a hollow cylinder. These toys are painted from inside. Out of the two, whose cost of painting at 1.50 per cm² is more and by how much? total h of toy 2 is 13 cm.
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For Toy 1:
- Surface area of the cone: π * r * l, where r is the radius and l is the slant height.
- Surface area of the hemisphere: 2 * π * r² (since only the curved surface is considered).
For Toy 2:
- Surface area of the hemisphere: 2 * π * r².
- Surface area of the hollow cylinder: 2 * π * (R + r) * h, where R is the outer radius, r is the inner radius, and h is the height.
Compare the total surface areas of both toys, and then calculate the cost difference based on the given cost per cm².
Answer:
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To find the cost of painting for each toy, we need to calculate the surface area of each toy and then multiply it by the cost per square centimeter.
### Toy 1:
Toy 1 consists of a cone mounted on a hemisphere. The total height of the toy is given, and we need to find the surface area.
#### Surface Area of Cone (A₁):
\[ A₁ = πr₁l₁ \]
where \( r₁ \) is the radius of the cone and \( l₁ \) is the slant height.
\[ l₁ = \sqrt{r₁² + h²} \]
#### Surface Area of Hemisphere (A₂):
\[ A₂ = 2πr₂² \]
where \( r₂ \) is the radius of the hemisphere.
#### Total Surface Area of Toy 1:
\[ Total\_Area\_Toy1 = A₁ + A₂ \]
### Toy 2:
Toy 2 consists of a hemispherical bowl mounted on a hollow cylinder. The total height of the toy is given.
#### Surface Area of Hemisphere (A₃):
\[ A₃ = 2πr₃² \]
where \( r₃ \) is the radius of the hemisphere.
#### Curved Surface Area of Hollow Cylinder (A₄):
\[ A₄ = 2πrh \]
where \( r \) is the outer radius of the cylinder, and \( h \) is the height.
#### Total Surface Area of Toy 2:
\[ Total\_Area\_Toy2 = A₃ + A₄ \]
Now, calculate the total surface areas and then find the cost of painting for each toy by multiplying with the cost per square centimeter.
\[ \text{Cost of Painting Toy 1} = Total\_Area\_Toy1 \times 1.50 \]
\[ \text{Cost of Painting Toy 2} = Total\_Area\_Toy2 \times 1.50 \]