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A hemi sphere of radius of 7 cm is surmounted on a cylinder of same radius and height 7 cm, then find it’s curved surface area ( in sq.cm) ?
- a)616
- b)620
- c)600
- d)626
Correct answer is option 'A'. Can you explain this answer?
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A hemi sphere of radius of 7 cm is surmounted on a cylinder of same ra...
So the answer is option A.
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A hemi sphere of radius of 7 cm is surmounted on a cylinder of same ra...
Curved Surface Area of the Composite Shape
To find the curved surface area of the composite shape (a hemisphere surmounted on a cylinder), we need to calculate the areas of the cylinder and the hemisphere separately, then sum them up.
1. Curved Surface Area of the Cylinder
- The formula for the curved surface area (CSA) of a cylinder is given by:
- CSA = 2 * π * r * h
- Here, r is the radius, and h is the height.
- For our cylinder:
- Radius (r) = 7 cm
- Height (h) = 7 cm
- Plugging in the values:
- CSA = 2 * π * 7 * 7 = 98π sq.cm
2. Curved Surface Area of the Hemisphere
- The formula for the curved surface area of a hemisphere is:
- CSA = 2 * π * r²
- For our hemisphere:
- Radius (r) = 7 cm
- Plugging in the values:
- CSA = 2 * π * (7)² = 98π sq.cm
3. Total Curved Surface Area
- Now, to find the total curved surface area of the composite shape, we add the CSA of the cylinder and the CSA of the hemisphere:
- Total CSA = CSA of Cylinder + CSA of Hemisphere
- Total CSA = 98π + 98π = 196π sq.cm
4. Numerical Approximation
- Using π ≈ 3.14:
- Total CSA = 196 * 3.14 ≈ 615.44 sq.cm
- Rounding this gives approximately 616 sq.cm.
Conclusion
Thus, the curved surface area of the composite shape is approximately 616 sq.cm, confirming that the correct answer is option 'A'.
To find the curved surface area of the composite shape (a hemisphere surmounted on a cylinder), we need to calculate the areas of the cylinder and the hemisphere separately, then sum them up.
1. Curved Surface Area of the Cylinder
- The formula for the curved surface area (CSA) of a cylinder is given by:
- CSA = 2 * π * r * h
- Here, r is the radius, and h is the height.
- For our cylinder:
- Radius (r) = 7 cm
- Height (h) = 7 cm
- Plugging in the values:
- CSA = 2 * π * 7 * 7 = 98π sq.cm
2. Curved Surface Area of the Hemisphere
- The formula for the curved surface area of a hemisphere is:
- CSA = 2 * π * r²
- For our hemisphere:
- Radius (r) = 7 cm
- Plugging in the values:
- CSA = 2 * π * (7)² = 98π sq.cm
3. Total Curved Surface Area
- Now, to find the total curved surface area of the composite shape, we add the CSA of the cylinder and the CSA of the hemisphere:
- Total CSA = CSA of Cylinder + CSA of Hemisphere
- Total CSA = 98π + 98π = 196π sq.cm
4. Numerical Approximation
- Using π ≈ 3.14:
- Total CSA = 196 * 3.14 ≈ 615.44 sq.cm
- Rounding this gives approximately 616 sq.cm.
Conclusion
Thus, the curved surface area of the composite shape is approximately 616 sq.cm, confirming that the correct answer is option 'A'.
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A hemi sphere of radius of 7 cm is surmounted on a cylinder of same radius and height 7 cm, then find it’s curved surface area ( in sq.cm) ?a)616b)620c)600d)626Correct answer is option 'A'. Can you explain this answer?
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