Question

find the volume and surface area of the orange. the orange was sliced in half, and the diameter is given. 8 cm (in the image of the sliced orange). round answer to 2 decimal places if needed. surface area of orange peel = blank volume of orange = blank question help: video 1 video 2 message instructor submit question

Explanation:

Step1: Find the radius of the orange

The diameter of the orange is 8 cm, so the radius \( r = \frac{d}{2} = \frac{8}{2} = 4 \) cm.

Step2: Calculate the surface area of the orange (sphere)

The formula for the surface area of a sphere is \( SA = 4\pi r^2 \).
Substitute \( r = 4 \) into the formula: \( SA = 4\pi (4)^2 = 4\pi \times 16 = 64\pi \approx 64 \times 3.1416 \approx 201.06 \) \( cm^2 \).

Step3: Calculate the volume of the orange (sphere)

The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \).
Substitute \( r = 4 \) into the formula: \( V = \frac{4}{3}\pi (4)^3 = \frac{4}{3}\pi \times 64 = \frac{256}{3}\pi \approx \frac{256}{3} \times 3.1416 \approx 268.08 \) \( cm^3 \).

Answer:

Surface Area of Orange Peel = \( 201.06 \) \( cm^2 \)
Volume of Orange = \( 268.08 \) \( cm^3 \)