Volume of the cone = 1/3 pi r^2 h = 1005.31 cm^3
Volume of the sphere = 4/3 pi r^3 = 463.25 cm^3
Volume of remaining portion of the cone = 1005.31 - 463.25
= 542.1 cm^3 to nearest tenth
Answer:
Remaining volume of carved is 542.06 (approx 542) cm³
Step-by-step explanation:
A sphere with a radius of 4.8 cm is carved out of a right cone with base of 8 cm and a height of 15 cm.
We need to find the remaining portion of the cone.
Remaining volume = Volume of cone - Volume of sphere
First we find volume of cone
Volume of cone [tex]=\frac{1}{3}\times \pi \times r^2\times h[/tex]
Volume of cone [tex]=\frac{1}{3}\times \pi \times 8^2\times 15\approx 1005.31\text{ cm}^3[/tex]
Now we find volume of sphere
Volume of sphere [tex]=\frac{4}{3}\times \pi \times r^3[/tex]
Volume of sphere [tex]=\frac{4}{3}\times \pi \times 4.8^3\approx 463.25\text{ cm}^3[/tex]
Remaining volume = 1005.31-463.25 = 542.06 cm³
Hence, Remaining volume of carved is 542.06 cm³
