Respuesta :
Answer:
For the first cone: r = 7 cm, h = 21 cm
For the second cone: r = 8 cm, h = 24 cm
Step-by-step explanation:
The volume of the first cone is [tex]343\pi cm^3[/tex]
The volume of the second cone is [tex]512\pi cm^3[/tex]
We are told that the height of each cone is 3 times its radius, hence:
h = 3r
The volume of a cone is given as:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Substituting h = 3r:
[tex]V = \frac{1}{3} \pi r^2(3r)\\\\\\V = \frac{1}{3} \pi (3r^3)\\\\\\V = \pi r^3[/tex]
For the first cone, V = [tex]343\pi cm^3[/tex], radius, r, will be:
[tex]343\pi = \pi r^3\\\\\\=> r^3 = 343\\\\\\r = \sqrt[3]{343} \\\\\\r = 7 cm[/tex]
∴ Its height will be:
h = 3r = 3 * 7 = 21 cm
For the second cone, V = [tex]512\pi cm^3[/tex], radius, r, will be:
[tex]512\pi = \pi r^3\\\\\\=> r^3 = 512\\\\\\r = \sqrt[3]{512} \\\\\\r = 8 cm[/tex]
∴ Its height will be:
h = 3r = 3 * 8 = 24 cm
The radius and height of the first cone are 7 cm and 21 cm respectively while the radius and height of the second cone are 8 cm and 24 cm respectively.
