Multiple choice

The curved surface area of a hemisphere is $\displaystyle 905! \frac{1}{7}! \ \text{cm}^2$, what is its volume?

  1. $3580.57 \,\text{cm}^3$
  2. $8220.57 \,\text{cm}^3$
  3. $8830.57 \,\text{cm}^3$
  4. $3620.57 \,\text{cm}^3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The curved surface area of a hemisphere is 2*pi*r^2 = 6337/7. Solving for r^2 gives r^2 = 6337 / (14 * pi) approx 144, so r = 12. The volume is (2/3)*pi*r^3 = (2/3)*pi*1728 = 1152*pi, which is approximately 3619.11. Option D is the closest value.

AI explanation

Convert the mixed fraction 905 1/7 to the improper fraction 6336/7. Using the curved surface area formula for a hemisphere, 2*pi*r^2 = 6336/7, and substituting pi as 22/7, we get r^2 = 144. This gives a radius of 12 cm. The volume of a hemisphere is (2/3) * pi * r^3, which calculates to (2/3) * (22/7) * 12^3 = 3620.57 cm^3.

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