Question

Marcus has been working on a large rubber band ball. When Marcus first measured the ball it had a diameter of 5 inches. Over the course of one year Marcus continued to add more rubber bands to the ball. After one year Marcus measured the rubber band ball, and it had a diameter of 15 inches. How much volume was added on to the rubber band ball? Round your answer to the nearest tenth. A 20.8π inches3 B 541.7π inches3 C 562.5π inches3 D 4333.3π inches3

Answer 1

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Answer 2

Answer:

The correct option is B. 541.7 inches³

Step-by-step explanation:

Diameter of the ball when first measured = 5 inches

So, Radius of the ball = 2.5 inches

The ball is in the shape of sphere

$\implies\text{Volume of the ball = }\frac{4}{3}\pi\times (2.5)^3$

Diameter of the ball measured after one year = 15 inches

So, Radius of the ball = 7.5 inches

$\implies\text{Volume of the ball = }\frac{4}{3}\pi\times (7.5)^3$

$\text{Now, increase in the volume = }\frac{4}{3}\pi\times (7.5)^3-\frac{4}{3}\pi\times (2.5)^3\\\\=\frac{4}{3}\pi(421.875 - 15.625)\\\\=\frac{4}{3}\pi\times 406.25\\\\=541.66 \pi \\\\\approx 541.7\pi\:\:inches^3$

Therefore, The correct option is B. 541.7 inches³