Question

a sphere is shown below. what is its approximate volume? (show your work for credit)
2.7 cm
\\(\bigcirc\\) \\(6.5\pi\\ \text{cm}^3\\)
\\(\bigcirc\\) \\(9\pi\\ \text{cm}^3\\)
\\(\bigcirc\\) \\(26\pi\\ \text{cm}^3\\)
\\(\bigcirc\\) \\(82\pi\\ \text{cm}^3\\)

Explanation:

Step1: Recall sphere volume formula

The volume $V$ of a sphere is $V = \frac{4}{3}\pi r^3$, where $r$ is the radius.

Step2: Substitute radius $r=2.7$ cm

$$V = \frac{4}{3}\pi (2.7)^3$$

Step3: Calculate $(2.7)^3$

$2.7^3 = 2.7 \times 2.7 \times 2.7 = 19.683$

Step4: Compute the coefficient

$\frac{4}{3} \times 19.683 = 26.244$

Step5: Approximate the value

$26.244\pi \approx 26\pi$

Answer:

C. $26\pi$ cm³