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Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of 15 centimeters (cm), and the smaller mug has an internal height of 10cm. Both mugs have an internal diameter of 8cm. Which of the following is closest to the difference in cubic centimeters (cm^(3)) between the internal volume of the larger mug and the internal volume of the smaller mug? Choose 1 answer: (A) 63cm^(3) (B) 251cm^(3) (C) 754cm^(3) (D) 1,005cm^(3)

Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of 15 cm15\,\text{cm}, and the smaller mug has an internal height of 10 cm10\,\text{cm}. Both mugs have an internal diameter of 8 cm8\,\text{cm}. Which of the following is closest to the difference in cubic centimeters (cm3)(\text{cm}^3) between the internal volume of the larger mug and the internal volume of the smaller mug?\newlineChoose 11 answer:\newline(A) 63 cm363\,\text{cm}^3\newline(B) 251 cm3251\,\text{cm}^3\newline(C) 754 cm3754\,\text{cm}^3\newline(D) 1,005 cm31,005\,\text{cm}^3

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Q. Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of 15 cm15\,\text{cm}, and the smaller mug has an internal height of 10 cm10\,\text{cm}. Both mugs have an internal diameter of 8 cm8\,\text{cm}. Which of the following is closest to the difference in cubic centimeters (cm3)(\text{cm}^3) between the internal volume of the larger mug and the internal volume of the smaller mug?\newlineChoose 11 answer:\newline(A) 63 cm363\,\text{cm}^3\newline(B) 251 cm3251\,\text{cm}^3\newline(C) 754 cm3754\,\text{cm}^3\newline(D) 1,005 cm31,005\,\text{cm}^3
  1. Calculate Volume of Mugs: First, we need to calculate the volume of each mug. The volume of a cylinder is given by the formula V=πr2hV = \pi r^2 h, where rr is the radius and hh is the height. The radius is half the diameter, so for both mugs, the radius is 8 cm/2=4 cm8 \, \text{cm} / 2 = 4 \, \text{cm}.
  2. Volume of Larger Mug: Now, let's calculate the volume of the larger mug using the formula. The height of the larger mug is 15 cm15\,\text{cm}. So, the volume VlargerV_{\text{larger}} is π×(4 cm)2×15 cm\pi \times (4\,\text{cm})^2 \times 15\,\text{cm}.
  3. Volume Calculation: Performing the calculation for the larger mug gives us Vlarger=π×16 cm2×15 cm=π×240 cm3V_{\text{larger}} = \pi \times 16 \text{ cm}^2 \times 15 \text{ cm} = \pi \times 240 \text{ cm}^3. We can approximate π\pi as 3.143.14 for this calculation. So, Vlarger≈3.14×240 cm3≈753.6 cm3V_{\text{larger}} \approx 3.14 \times 240 \text{ cm}^3 \approx 753.6 \text{ cm}^3.
  4. Volume of Smaller Mug: Next, we calculate the volume of the smaller mug. The height of the smaller mug is 10 cm10\,\text{cm}. So, the volume VsmallerV_{\text{smaller}} is π×(4 cm)2×10 cm.\pi \times (4\,\text{cm})^2 \times 10\,\text{cm}.
  5. Volume Calculation: Performing the calculation for the smaller mug gives us Vsmaller=π×16 cm2×10 cm=π×160 cm3V_{\text{smaller}} = \pi \times 16 \text{ cm}^2 \times 10 \text{ cm} = \pi \times 160 \text{ cm}^3. Using the approximation for π\pi, Vsmaller≈3.14×160 cm3≈502.4 cm3V_{\text{smaller}} \approx 3.14 \times 160 \text{ cm}^3 \approx 502.4 \text{ cm}^3.
  6. Find Difference in Volume: To find the difference in volume between the two mugs, we subtract the volume of the smaller mug from the volume of the larger mug: Difference=Vlarger−Vsmaller\text{Difference} = V_{\text{larger}} - V_{\text{smaller}}.
  7. Subtract Volumes: Subtracting the volumes gives us Difference ≈753.6 cm3−502.4 cm3≈251.2 cm3\approx 753.6 \, \text{cm}^3 - 502.4 \, \text{cm}^3 \approx 251.2 \, \text{cm}^3. Rounding to the nearest whole number, the difference is approximately 251 cm3251 \, \text{cm}^3.

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