The total surface area of a hemispherical bowl of radius 77 cm isa)55902 cm2b)55900 cm2c)50002 cm2d)45602 cm2Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Option A is correct

Answer

A

Answer

Answer

TSA of hemisphere =3πr²
= 3x22/7x77x77
=66x11x77
=726x77
=55902cm²

Answer

To find the total surface area of a hemispherical bowl, we need to calculate the curved surface area and the base area separately and then add them together.

**Curved Surface Area**
The curved surface area of a hemisphere is given by the formula: CS = 2πr^2, where r is the radius of the hemisphere.

Given that the radius of the hemispherical bowl is 77 cm, we can substitute this value into the formula to find the curved surface area:
CS = 2π(77)^2
CS = 2π(5929)
CS = 11858π cm^2

**Base Area**
The base of the hemispherical bowl is a circle with radius r. The formula for the area of a circle is: A = πr^2.

Substituting the radius of the hemispherical bowl into the formula, we can find the base area:
A = π(77)^2
A = π(5929)
A = 5929π cm^2

**Total Surface Area**
To find the total surface area, we need to add the curved surface area and the base area together:
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area = 11858π + 5929π
Total Surface Area = 17787π cm^2

Now, to find the value of the total surface area, we can use the approximation π ≈ 3.14:
Total Surface Area ≈ 17787 × 3.14
Total Surface Area ≈ 55842.18 cm^2

Rounding the value to the nearest whole number, we get the total surface area of the hemispherical bowl as approximately 55902 cm^2.

Therefore, the correct answer is option A) 55902 cm^2.

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