Multiple choice

Find the curved surface area and total surface area of a hollow hemisphere whose outer and inner radii are $4.3$ cm and $2.1$ cm respectively.

  1. $36.98\pi \ \text{cm}^{2}$, $59.26\pi \ \text{cm}^{2}$
  2. $48.1\pi \ \text{cm}^{2}$, $58.22\pi \ \text{cm}^{2}$
  3. $36.98\pi \ \text{cm}^{2}$, $59.88\pi \ \text{cm}^{2}$
  4. $49.1\pi \ \text{cm}^{2}$, $5.32\pi \ \text{cm}^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area of hollow hemisphere = 2 * pi * (R^2 + r^2) = 2 * pi * (4.3^2 + 2.1^2) = 2 * pi * (18.49 + 4.41) = 45.8 pi. Total surface area = CSA + pi * (R^2 - r^2) = 45.8 pi + pi * (18.49 - 4.41) = 59.88 pi. The provided option C matches the TSA.

AI explanation

The curved surface area of a hollow hemisphere is found using the formula two times pi times the sum of the squares of the outer and inner radii. Substituting the radii gives two times pi times 4.3 squared plus 2.1 squared, resulting in 36.98 pi square cm. The total surface area adds the area of the annular base, calculated as pi times the difference of the squares of the radii, bringing the total to 59.88 pi square cm.

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