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pochemuha
2 years ago
5

The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate,

she approximates π using 3 in both the surface area and volume formulas for a sphere.
Using this method, what value does she get for the approximate surface area of the sculpture?
Mathematics
1 answer:
Brrunno [24]2 years ago
3 0

Answer:

192 ft^2

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

\pi is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. Volume =\frac{4}{3}\pi r^3

2. Surface\ Area = 4\pi r^2

Given volume is 256 ft³.

256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}

So, approximate surface area of sculpture is 192 ft^2.

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