I need help please.

Question

Three different cones are used for the storage of food. They are related as follows:

• Cone A has radius of r and height of h. •

Cone B has 3 times the height of Cone A but has the same radius. •

Cone C has 4 times the radius of Can A but has the same height. A.

Determine the ratio, A:B:C, of the volumes of the cones?

B. What Knowledge do you apply for this question and what did you learn from this lesson?

Answer 1

Volume of a cone equation: V=(1/3)*π*r²*h

Volume of A: Cone A has radius of r and height of h.

Write equation representing volume of cone A:

V_a=(1/3)*π*r_a²*h_a

Volume of B: Cone B has 3 times the height of Cone A but has the same radius.

Write equation representing volume of cone B where the height is 3x the heights of cone A:

V_b=(1/3)*π*r_b²*h_b

h_b = 3h_a and r_b = r_a

V_b=(1/3)*π*r_a²*(3h_a)

V_b=(1/3)*(3)*π*r_a²*(h_a) = π*r_a²*h_a

Volume B = 3x Volume A

Volume of C: Cone C has 4 times the radius of Cone A but has the same height of A.

Write equation representing volume of cone C where the radius is 4x the radius of cone A:

V_c=(1/3)*πr_c²*h_c

r_c = 4h_a and h_c = h_a

V_c=(1/3)*π*(4r_a)²*h_a

V_c=(1/3)*π*16*r_a²*h_a = (16/3)*π*r_a²*h_a

Volume C = 16/3 x Volume A

Ratio of volume:

A:B:C

1 : 3 : 16/3 or 3:9:16

This problem involves substitution based on relationships of dimensions between the cones.