Question

Your brain is arguably the most complex known system. The typical human brain is 3 times the volume of a typical human breath. It is 21 times the volume of an Apple iPhone 4. If your brain were a cube, the edge length of a side would be 4.3 inches, or about one-third of a foot. If your brain were a sphere with a radius of 2.7 inches, what would be its volume?

a) 79 in³
b) 21 in³
c) 12.9in³
d) 4 in³

Answer 1

The volume of a sphere with a radius of 2.7 inches is calculated using the formula V = (4/3)πr^3. Upon performing the calculations, the volume is approximately 82.5 cubic inches, which is not represented in any of the given answer choices.

Step-by-step explanation:

To calculate the volume of a sphere with a radius of 2.7 inches, we use the formula for the volume of a sphere, which is V = \(\frac{4}{3}\)\pi r^3, where V represents the volume and r is the radius of the sphere. Plugging in our value for the radius, we get:

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

Calculating this out:

V = \(\frac{4}{3}\)\pi (19.683)

V = \(\frac{4}{3}\) * 3.14159 * 19.683

V = 4.18879 * 19.683

V ≈ 82.477 cubic inches

The volume is approximately 82.5 cubic inches, which would round to 82 when considering significant figures. None of the given answer choices (a) 79 in³, (b) 21 in³, (c) 12.9 in³, or (d) 4 in³ are correct.