Question

1. choose the scenario where the volume calculations result in less than 200 cubic units.

a. sphere with a radius of 4 units
b. pyramid with a square base of side 10 units and a height of 15 units
c. cone with a radius of 3 units and a height of 4 units
d. cone with a radius of 10 units and a height of 3 units

Explanation:

Step1: Volume of sphere formula

$V_{sphere}=\frac{4}{3}\pi r^{3}$
Substitute $r = 4$: $V=\frac{4}{3}\pi(4)^{3}=\frac{4}{3}\pi\times64=\frac{256\pi}{3}\approx268.08>200$

Step2: Volume of pyramid formula

$V_{pyramid}=\frac{1}{3}Bh$ (where $B$ is base area). For square base $B = s^{2}=10^{2} = 100$, $h = 15$. Then $V=\frac{1}{3}\times100\times15 = 500>200$

Step3: Volume of cone formula

$V_{cone}=\frac{1}{3}\pi r^{2}h$
For option C: $r = 3$, $h = 4$. Then $V=\frac{1}{3}\pi(3)^{2}\times4=\frac{1}{3}\pi\times9\times4 = 12\pi\approx37.7<200$

Step4: For option D

$r = 10$, $h = 3$. Then $V=\frac{1}{3}\pi(10)^{2}\times3= 100\pi\approx314.16>200$

Answer:

C. Cone with a radius of 3 units and a height of 4 units