To find the outer curved surface area of the bowl, we need to calculate the surface area of the outer hemisphere and subtract the surface area of the inner hemisphere.
Given:
Inner radius (r) = 5 cm
Thickness of the steel (t) = 0.25 cm
The outer radius (R) can be calculated by adding the inner radius and the thickness:
R = r + t = 5 cm + 0.25 cm = 5.25 cm
The surface area of a hemisphere is given by the formula:
A = 2πR^2
The surface area of the outer hemisphere is:
A_outer = 2πR^2 = 2π(5.25 cm)^2
The surface area of the inner hemisphere is:
A_inner = 2πr^2 = 2π(5 cm)^2
The outer curved surface area of the bowl is the difference between the two surface areas:
Answers & Comments
Answer:
To find the outer curved surface area of the bowl, we need to calculate the surface area of the outer hemisphere and subtract the surface area of the inner hemisphere.
Given:
Inner radius (r) = 5 cm
Thickness of the steel (t) = 0.25 cm
The outer radius (R) can be calculated by adding the inner radius and the thickness:
R = r + t = 5 cm + 0.25 cm = 5.25 cm
The surface area of a hemisphere is given by the formula:
A = 2πR^2
The surface area of the outer hemisphere is:
A_outer = 2πR^2 = 2π(5.25 cm)^2
The surface area of the inner hemisphere is:
A_inner = 2πr^2 = 2π(5 cm)^2
The outer curved surface area of the bowl is the difference between the two surface areas:
Outer surface area = A_outer - A_inner = 2π(5.25 cm)^2 - 2π(5 cm)^2
Calculating this expression:
Outer surface area = 2π(5.25^2 - 5^2) cm^2
Simplifying further:
Outer surface area = 2π(27.5625 - 25) cm^2
Outer surface area ≈ 2π(2.5625) cm^2
Outer surface area ≈ 2π(2.5625) cm^2
Outer surface area ≈ 16.063 cm^2 (approximate value)
Therefore, the outer cover surface area of the hemispherical bowl is approximately 16.063 square centimeters.
Step-by-step explanation:
hope that helps!
Verified answer
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Inner radius of hemispherical bowl = 5 cm
Thickness of the bowl = 0.25 cm
∴ Outer radius (r) of hemispherical bowl = (5 + 0.25) cm
= 5.25 cm
Outer CSA of hemispherical bowl =
[tex]2\pi \: {r}^{2} [/tex]
[tex]2 \times \frac{22}{7} \times (5.25cm) {}^{2} = 173.25[/tex]
Therefore, the outer curved surface area of the bowl is 173.25 cm2.