Question

A sphere of surface area 500𝝅 square centimeters is cut into two equal hemispheres. The surface area of each hemisphere in square centimeters is

• A. 250𝝅
• B. 500𝝅
• C. 375𝝅
• D. 125𝝅

Answer 1

Answer:

C. 375𝝅

Sphere and Hemisphere Surface Area Calculations

Sphere Properties

• The surface area of a sphere is given by the formula A = 4πr², where 'r' is the radius.

• Given surface area of the sphere is 500π square centimeters.

• Therefore, 4πr² = 500π.

• Solving for r²: r² = 500π / 4π = 125.

• Thus, the radius 'r' of the sphere is √125 cm.

Hemisphere Properties

• When a sphere is cut into two equal hemispheres, each hemisphere has two surfaces:

  1. The curved surface area, which is half the surface area of the original sphere.

  2. The flat circular base area, which is created by the cut.

• Curved surface area of one hemisphere = (1/2) × (Surface area of sphere) = (1/2) × 500π = 250π square centimeters.

• Area of the circular base = πr².

• From the sphere's calculation, we found r² = 125.

• So, the area of the circular base = 125π square centimeters.

• Total surface area of one hemisphere = Curved surface area + Area of circular base

• Total surface area = 250π + 125π = 375π square centimeters.