Question

find the surface area of this sphere. use 3.14 for π. 8 cm surface area of a sphere sa = 4πr² sa = ? cm² round your answer to the nearest tenth

Explanation:

Answer:

To find the surface area of the sphere, we use the formula \( SA = 4\pi r^2 \), where \( r = 8 \) cm and \( \pi = 3.14 \).

First, substitute the values into the formula:
\( SA = 4 \times 3.14 \times 8^2 \)

Calculate \( 8^2 = 64 \):
\( SA = 4 \times 3.14 \times 64 \)

Multiply \( 4 \times 3.14 = 12.56 \):
\( SA = 12.56 \times 64 \)

Calculate \( 12.56 \times 64 = 803.84 \)

Rounding to the nearest tenth, we get \( 803.8 \) (wait, actually, 803.84 rounded to the nearest tenth is 803.8? Wait, no—803.84 to the nearest tenth: the hundredth digit is 4, which is less than 5, so we keep the tenth digit as is. Wait, but 803.84 is 803.8 when rounded to the nearest tenth? Wait, no, 803.84: the tenths place is 8, hundredths is 4. So yes, 803.8. Wait, but let me check again:

Wait, \( 4 \times 3.14 = 12.56 \); \( 12.56 \times 64 \):

\( 12.56 \times 60 = 753.6 \)
\( 12.56 \times 4 = 50.24 \)
Adding them: \( 753.6 + 50.24 = 803.84 \)

Rounded to the nearest tenth: 803.8 (since the hundredth digit is 4, which is less than 5, we don't round up the tenth digit). Wait, but 803.84 is 803.8 when rounded to the nearest tenth? Wait, no—803.84: the tenths place is 8, hundredths is 4. So yes, 803.8. Wait, but maybe I made a mistake. Wait, 803.84 to the nearest tenth: the number is 803.84. The tenths digit is 8, the hundredths digit is 4. Since 4 < 5, we round down, so it's 803.8.

But wait, let me confirm the calculation again. The radius is 8 cm. So \( r = 8 \). Then \( SA = 4 \times 3.14 \times 8^2 = 4 \times 3.14 \times 64 \). Let's compute 3.14 64 first: 3.14 64 = 200.96. Then 4 * 200.96 = 803.84. So 803.84 rounded to the nearest tenth is 803.8.

Wait, but maybe the problem expects 803.8 or 803.84? Wait, the problem says "round your answer to the nearest tenth". So 803.84 rounded to the nearest tenth is 803.8.

So the surface area is \( \boxed{803.8} \) cm².