# What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?

###### Question:

## Answers

you have used the volume formula when the problem asks for a difference of area.

ΔA = 4π(2r+1) = 8πr +4π

Step-by-step explanation:

A(r) = 4πr²

ΔA = A(r+1) - A(r) = (4π(r+1)²) -4πr² = 4π(r² +2r +1 - r²)

ΔA = 4π(2r +1) = 8πr +4π

8πr + 4π

Step-by-step explanation:

Your mistake in solving this problem was using the formula for volume rather than find the difference in area.

a(r) = 4πr^2

a = a(r + 1) - a(r)

a = [4π(r + 1)^2]

a = 4π(r^2 - r^2 + 2r + 1)

a = 4π(2r + 1)

a = 8πr + 4π

Best of Luck!

The volume of the sphere of radius r is:

V1 = (4/3) * (pi) * (r ^ 3)

Where,

r: sphere radius:

The volume of the sphere of radius 0.3r is:

V2 = (4/3) * (pi) * ((0.3r) ^ 3)

Rewriting:

V2 = (4/3) * (pi) * (0.027 (r) ^ 3)

V2 = 0.027 (4/3) * (pi) * (r ^ 3)

V2 = 0.027V1

The difference is:

V1-V2 = V1-0.027V1 = V1 (1-0.027)

V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)

the difference in volume between a sphere with radius and a sphere with radius 0.3r is:

V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)

[tex]d = 1.2973\pi r^3[/tex]

Step-by-step explanation:

Given

[tex]R_1 = r[/tex]

[tex]R_2 = 0.3[/tex]

Required

The difference in their volumes

The volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

So, the difference d is:

[tex]d = \frac{4}{3}\pi [R_1^3 - R_2^3][/tex]

[tex]d = \frac{4}{3}\pi [r^3 - (0.3r)^3][/tex]

[tex]d = \frac{4}{3}\pi [r^3 - 0.027r^3][/tex]

[tex]d = \frac{4}{3}\pi *0.973r^3[/tex]

[tex]d = \frac{3.892}{3}\pi r^3[/tex]

[tex]d = 1.2973\pi r^3[/tex]

I’m tome

what is the graph

step-by-step explanation: