Math  /  Geometry

QuestionWhat is the surface area of this sphere? Use π3.14\pi \approx 3.14 and round your answer to the nearest hundredth. \square square inches

Studdy Solution

STEP 1

What is this asking? We need to find the total area of the outside of a perfectly round ball, given its radius. Watch out! Don't mix up radius and diameter!
The diameter is twice the radius, and we're given the *radius* here.

STEP 2

1. Recall the formula
2. Plug and chug

STEP 3

Alright, let's **kick things off** with the formula for the surface area of a sphere!
It's SA=4πr2SA = 4 \cdot \pi \cdot r^2, where SASA stands for **surface area** and rr is the **radius**.
This formula tells us how to calculate the total area covering the outside of a sphere.

STEP 4

Now, let's **plug in** our **radius**, which is r=1.7r = 1.7 inches.
So, we have SA=4π(1.7)2SA = 4 \cdot \pi \cdot (1.7)^2.

STEP 5

Next, let's **square** the **radius**: (1.7)2=1.71.7=2.89(1.7)^2 = 1.7 \cdot 1.7 = 2.89.
So, our formula becomes SA=4π2.89SA = 4 \cdot \pi \cdot 2.89.

STEP 6

We're given that we should use π3.14\pi \approx 3.14.
Let's **substitute** that in: SA=43.142.89SA = 4 \cdot 3.14 \cdot 2.89.

STEP 7

Time to **multiply**!
First, 43.14=12.564 \cdot 3.14 = 12.56.
Then, 12.562.89=36.298412.56 \cdot 2.89 = 36.2984.
So, SA36.2984SA \approx 36.2984 square inches.

STEP 8

Finally, we need to **round** our answer to the nearest hundredth.
The hundredths place is the second digit after the decimal point, which is 9.
Since the next digit is 8 (which is 5 or greater), we **round up**.
So, our **final answer** is approximately 36.3036.30 square inches.

STEP 9

The surface area of the sphere is approximately 36.3036.30 square inches.

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