Question 37

If a sphere of radius r is divided into four identical parts, then the total surface area of the four parts is

Solution

Sphere of radius r is divided into 4 identical parts

Radius of each part = r units

Each part has 1 curvedsurface and 2 semicircular faces

TSA of each part = 1/4 of curved surface area of sphere + 2 area of semicircular face

TSA = $$ \frac{1}{4} \times 4\pi r^2 + 2 \times \frac{1}{2} \pi r^2 = 2\pi r^2 $$

TSA of 4 parts = $$ 4 \times 2\pi r^2 = 8\pi r^ 2 $$

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