Question

mrs. norcross bought a pack of christmas tree decorations that includes ornaments shaped like spheres and cones. which ornament takes up less space in the box?$v=\frac{4}{3}\pi r^{3}LXB048,656\pi \text{cm}^{3}LXB115,552\pi \text{cm}^{3}$rewatch

Explanation:

Step1: Identify cone parameters

Radius $r = 24$ mm, height $h = 81$ mm

Step2: Substitute into cone volume formula

$V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (24)^2 (81)$

Step3: Calculate the numerical coefficient

First, $(24)^2 = 576$, then $\frac{1}{3} \times 576 \times 81 = 576 \times 27 = 15552$

Step4: Compare volumes

Sphere volume: $36000\pi$ mm³; Cone volume: $15552\pi$ mm³. $15552\pi < 36000\pi$

Answer:

The cone-shaped ornament takes up less space, with a volume of $15,552\pi$ mm³.
For the multiple-choice question, the correct option is: 15,552π cm³ (note: unit should be mm³, likely a typo in the option)