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If a right circular cone of height 24 cm has a volume of 1232 cm3, then the area of its curved surface is :
- a)154 cm2
- b)550 cm2
- c)704 cm2
- d)1254 cm2
Correct answer is option 'B'. Can you explain this answer?
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If a right circular cone of height 24 cm has a volume of 1232 cm3, the...
**Given:**
Height of the cone = 24 cm
Volume of the cone = 1232 cm^3
**To find:**
Area of the curved surface of the cone
**Solution:**
The volume of a cone is given by the formula:
Volume = (1/3) * π * r^2 * h
where r is the radius of the base and h is the height of the cone.
We are given the volume of the cone as 1232 cm^3, so we can write the equation as:
1232 = (1/3) * π * r^2 * 24
Simplifying the equation:
1232 = 8πr^2
r^2 = 1232/(8π)
r^2 = 49/π
r = √(49/π)
r ≈ 3.511 cm (approx)
**Calculating the slant height:**
The slant height of the cone can be calculated using the Pythagorean theorem:
Slant height^2 = radius^2 + height^2
Slant height^2 = (3.511)^2 + (24)^2
Slant height ≈ 24.764 cm (approx)
**Calculating the curved surface area:**
The curved surface area of the cone can be calculated using the formula:
Curved surface area = π * r * slant height
Curved surface area = π * 3.511 * 24.764
Curved surface area ≈ 275.437 cm^2 (approx)
Comparing the calculated curved surface area with the given options:
a) 154 cm^2
b) 550 cm^2
c) 704 cm^2
d) 1254 cm^2
The closest option to the calculated curved surface area is option b) 550 cm^2.
Therefore, the correct answer is option b) 550 cm^2.
Height of the cone = 24 cm
Volume of the cone = 1232 cm^3
**To find:**
Area of the curved surface of the cone
**Solution:**
The volume of a cone is given by the formula:
Volume = (1/3) * π * r^2 * h
where r is the radius of the base and h is the height of the cone.
We are given the volume of the cone as 1232 cm^3, so we can write the equation as:
1232 = (1/3) * π * r^2 * 24
Simplifying the equation:
1232 = 8πr^2
r^2 = 1232/(8π)
r^2 = 49/π
r = √(49/π)
r ≈ 3.511 cm (approx)
**Calculating the slant height:**
The slant height of the cone can be calculated using the Pythagorean theorem:
Slant height^2 = radius^2 + height^2
Slant height^2 = (3.511)^2 + (24)^2
Slant height ≈ 24.764 cm (approx)
**Calculating the curved surface area:**
The curved surface area of the cone can be calculated using the formula:
Curved surface area = π * r * slant height
Curved surface area = π * 3.511 * 24.764
Curved surface area ≈ 275.437 cm^2 (approx)
Comparing the calculated curved surface area with the given options:
a) 154 cm^2
b) 550 cm^2
c) 704 cm^2
d) 1254 cm^2
The closest option to the calculated curved surface area is option b) 550 cm^2.
Therefore, the correct answer is option b) 550 cm^2.
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If a right circular cone of height 24 cm has a volume of 1232 cm3, then the area of its curved surface is :a)154 cm2b)550 cm2c)704 cm2d)1254 cm2Correct answer is option 'B'. Can you explain this answer?
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