The volume of a sphere is given by the formula V=(4)/(3) πr^3, and its surface area by the formu

Name: Problem 50, Chapter :
Uploaded: 2020-08-06T01:21:34-08:00
Duration: 1 min 11 s
Channel: Lily An
Description: The volume of a sphere is given by the formula V=(4)/(3) πr^3, and its surface area by the formula S=4 πr^2, where r is the radius of the sphere. What is the surface area of a sphere, in square inches, if its volume is (2,048 π)/(3) ? A. 32 π?. 144 πC. 256 πD. 324 πE. 512 π

step 1 Okay, so for this one, it tells us that the volume of a sphere is 4 over 3 pi r cubed, and it sa

Question

The volume of a sphere is given by the formula $V=\frac{4}{3} \pi r^{3},$ and its surface area by the formula $S=4 \pi r^{2},$ where $r$ is the radius of the sphere. What is the surface area of a sphere, in square inches, if its volume is $\frac{2,048 \pi}{3} ?$ A. $32 \pi$ ?. $144 \pi$ C. $256 \pi$ D. $324 \pi$ E. $512 \pi$

   The volume of a sphere is given by the formula $V=\frac{4}{3} \pi r^{3},$ and its surface area by the formula $S=4 \pi r^{2},$ where $r$ is the radius of the sphere. What is the surface area of a sphere, in square inches, if its volume is $\frac{2,048 \pi}{3} ?$
A. $32 \pi$
?. $144 \pi$
C. $256 \pi$
D. $324 \pi$
E. $512 \pi$

Instant Answer

Solved by Expert Lily An

08/06/2020

Step 1

We can set this equal to the formula for the volume of a sphere, $\frac{4}{3} \pi r^{3}$, and solve for $r$: \[\frac{2048 \pi}{3} = \frac{4}{3} \pi r^{3}\] Show more…

Show all steps

Thanks for your feedback!

The volume of a sphere is given by the formula $V=\frac{4}{3} \pi r^{3},$ and its surface area by the formula $S=4 \pi r^{2},$ where $r$ is the radius of the sphere. What is the surface area of a sphere, in square inches, if its volume is $\frac{2,048 \pi}{3} ?$ A. $32 \pi$ ?. $144 \pi$ C. $256 \pi$ D. $324 \pi$ E. $512 \pi$

Play audio

Feedback

Lily An and 68 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Algebraic Manipulation

Algebraic techniques, such as isolating variables and taking cube roots, are used to rearrange the sphere's volume formula to solve for the radius, which is then applied in the surface area formula.

Surface Area Formula for a Sphere

The surface area of a sphere is determined using the formula S = 4?r^2. Knowing the radius from the volume calculation enables the computation of the sphere's surface area.

Sphere Geometry

Sphere geometry concerns the study of three-dimensional objects where all points are equidistant from a central point. This includes understanding and applying formulas for the volume and surface area of a sphere.

Volume Formula for a Sphere

The volume of a sphere is calculated using the formula V = (4/3)?r^3. This relation connects the radius of the sphere with its volume and allows one to solve for the radius when the volume is known.

Please give Ace some feedback