Answer:
Question 1.
- a) [tex]V=96\pi m^3[/tex]
Question 2:
[tex]V=1,648.5ft^3[/tex]
Question 3:
[tex]V=1,674.7cm^3[/tex]
Explanation:
Question 1. In the cone below, the radius is 6 meters and the height is 8 meters.
A) Find the exact value of the volume of the cone.
Formula:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Plug in r = 6m, and h = 8m
[tex]V=\dfrac{1}{3}\pi (6m)^2(8m)\\\\\\ V=\dfrac{1}{3}(36)(8)\pi m^3[/tex]
Solution:
[tex]V=96\pi m^3[/tex]
B) Find the approximate value of the volume of the cone rounded to the nearest tenth.
Substitute π with its approximate value 3.14
[tex]V=96(3.14)m^3\\\\V=301.4m^3[/tex]
Question 2. Find the volume of the cylinder pictured below. Use 3.14 for pi. Give your answer rounded to the nearest tenth.
Formula
[tex]V=\pi\times (\dfrac{diameter}{2})^2\times height[/tex]
Plug in diameter = 10 ft, height = 21, and π = 3.14
[tex]V=3.14\times (\dfrac{10}{2})^2\times 21ft\\\\V=3.14\times 25ft\times 21ft[/tex]
Solution:
[tex]V=1,648.5ft^3[/tex]
Question 3. Find the volume of the sphere pictured below. The sphere has a radius of 20 cm. Use 3.14 for pi. Give your answer rounded to the nearest tenth.
Formula
[tex]V==\dfrac{4}{3}\pi r^3[/tex]
Plug in r = 20cm, and π = 3.14
[tex]V=\dfrac{4}{3}\times 3.14\times (20cm)^3[/tex]
Solution:
[tex]V=1,674.7cm^3[/tex]
