The total surface area of a hemispherical bowl is the sum of its base area and its lateral surface area. The base area is the area of the circular base of the bowl, while the lateral surface area is the area of the curved surface of the bowl.

Given that the total surface area of one bowl is 96 cm², we can find the lateral surface area of one bowl by subtracting the base area from the total surface area. Let's assume the base area is B and the lateral surface area is L.


The base area of a hemisphere is given by the formula:
B = πr²
where r is the radius of the hemisphere.

In this case, we have the total surface area of one bowl, which includes the base area. So, we need to subtract the lateral surface area from the total surface area to find the base area.

Total surface area = Base area + Lateral surface area
96 cm² = B + L


We know that the lateral surface area of a hemisphere is given by the formula:
L = 2πr²


To find the radius of the hemisphere, we need to use the formula for the total surface area of a hemisphere:
Total surface area = 3πr²
96 cm² = 3πr²

Simplifying the equation, we get:
r² = 96 cm² / (3π)
r² = 32 cm² / π
r ≈ √(32 / π)
r ≈ √(32 / 3.1415)
r ≈ √(10.1913)
r ≈ 3.1937 cm


Now that we have the radius of one bowl, we can find the lateral surface area of one bowl using the formula:
L = 2πr²

To find the lateral surface area of 5 bowls, we simply multiply the lateral surface area of one bowl by 5:
Lateral surface area of 5 bowls = 5L

Substituting the value of r, we get:
Lateral surface area of 5 bowls ≈ 5(2π(3.1937)²)
≈ 5(2π(10.1913))
≈ 5(20.3826π)
≈ 101.913π cm²

Approximating the value of π to 3.1415, we get:
≈ 101.913(3.1415)
≈ 320.326 cm²

Therefore, the lateral surface area of 5 such bowls is approximately 320 cm², which corresponds to option A.

Option A