If the radius of the base and the height of a right circular cone are respectively 21 cm and 28 cm, then the curved surface area of the cone is (Take π = 22/7)a)3696 cm2b)2310cm2c)2550cm2d)2410cm2Correct answer is option 'B'. Can you explain this answer?

Question

If the radius of the base and the height of a right circular cone are respectively 21 cm and 28 cm, then the curved surface area of the cone is (Take &pi; = 22/7)a)3696 cm2b)2310cm2c)2550cm2d)2410cm2Correct answer is option 'B'. Can you explain this answer?

Answer

For a cone, l=h^2+rr^2 whole root , where h is the height.
Hence, l=28^2+212^2 whole root

l=35 cm

Curved surface area of a cone =πrl where r is the radius of the cone and l is the slant height.
Hence, curved surface area of this cone =722×21×35=2310cm^2

Answer

Answer

The curved surface area of a cone can be calculated using the formula:

CSA = π * r * l

where CSA is the curved surface area, r is the radius of the base, and l is the slant height of the cone.

To find the slant height, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the slant height (l) is the hypotenuse, and the radius (r) is one of the other sides. The height (h) is the other side.

Using the Pythagorean theorem, we can calculate the slant height (l):

l^2 = r^2 + h^2
l^2 = 21^2 + 28^2
l^2 = 441 + 784
l^2 = 1225
l = √1225
l = 35 cm

Now, we can substitute the values of the radius (r = 21 cm) and the slant height (l = 35 cm) into the formula for the curved surface area:

CSA = π * r * l
CSA = π * 21 cm * 35 cm
CSA = 735π cm^2

Therefore, the curved surface area of the cone is 735π cm^2.

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