The surface area of the right circular cone topped with hemisphere is? 2cm radius and 4cm height
π/3 * 2^2 * 4 + 2π/3 * 2^3 = 32/3 π
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To find the surface area of a right circular cone topped with a hemisphere, we need to calculate the surface area of the cone and the surface area of the hemisphere separately, then add them together.
Surface area of the cone:
The formula to calculate the surface area of a cone is given by:
A_cone = πr_cone * (r_cone + √(r_cone^2 + h_cone^2))
Given that the radius (r_cone) is 2 cm and the height (h_cone) is 4 cm, we can substitute these values into the formula:
A_cone = π * 2 * (2 + √(2^2 + 4^2))
A_cone = π * 2 * (2 + √(4 + 16))
A_cone = π * 2 * (2 + √20)
A_cone ≈ 6.28 * (2 + √20)
A_cone ≈ 6.28 * (2 + 4.47)
A_cone ≈ 6.28 * 6.47
A_cone ≈ 40.61 cm²
Surface area of the hemisphere:
The formula for the surface area of a hemisphere is given by:
A_hemisphere = 2πr^2
Given the radius of the hemisphere is also 2 cm, we can substitute this value into the formula:
A_hemisphere = 2π * (2^2)
A_hemisphere = 2π * 4
A_hemisphere ≈ 25.13 cm²
Therefore, the total surface area of the right circular cone topped with a hemisphere is:
Total surface area = Surface area of cone + Surface area of hemisphere
Total surface area ≈ 40.61 cm² + 25.13 cm²
Total surface area ≈ 65.74 cm²
So, the surface area of the right circular cone topped with a hemisphere is approximately 65.74 cm².
To find the surface area of a right circular cone topped with a hemisphere, you need to calculate the surface area of the cone and add it to the surface area of the hemisphere.
First, let's find the surface area of the cone. The formula for the surface area of a cone is:
S₁ = πr₁ℓ + πr₁²
Where:
- S₁ is the surface area of the cone
- r₁ is the radius of the base of the cone
- ℓ is the slant height of the cone
Given:
- r₁ = 2 cm (radius of the cone)
To find the slant height (ℓ) of the cone, we can use the Pythagorean theorem:
- ℓ² = r₁² + h₁²
Given:
- h₁ = 4 cm (height of the cone)
Substituting the known values into the equation, we have:
ℓ² = (2 cm)² + (4 cm)²
ℓ² = 4 cm² + 16 cm²
ℓ² = 20 cm²
ℓ = √20 cm ≈ 4.47 cm (rounded to two decimal places)
Now we can find the surface area of the cone:
S₁ = π(2 cm)(4.47 cm) + π(2 cm)²
S₁ = 8π cm² + 4π cm²
S₁ = 12π cm²
Next, let's find the surface area of the hemisphere. The formula for the surface area of a hemisphere is:
S₂ = 2πr₂²
Where:
- S₂ is the surface area of the hemisphere
- r₂ is the radius of the hemisphere
Given:
- r₂ = 2 cm (radius of the hemisphere)
Substituting the known value into the equation, we have:
S₂ = 2π(2 cm)²
S₂ = 2π(4 cm²)
S₂ = 8π cm²
Finally, to find the total surface area, we add the surface area of the cone and the surface area of the hemisphere:
Total Surface Area = S₁ + S₂
Total Surface Area = 12π cm² + 8π cm²
Total Surface Area = 20π cm²
Therefore, the surface area of the right circular cone topped with a hemisphere is 20π cm².