Suppose a spherical asteroid has a radius of approximately 9.0 x 10^2m. Use the formula 4/3*pi
r^3 to find the approximate volume of the asteroid.
2.57 * 10^9 m^3
1.07 * 10^4 m^3
2.54 * 10^10 m^3
4.51 * 10^10 m^3
I've worked 4/3*pi*10^2 = 900 meters... but now I'm confused, but I know it's something to do with 900^3... please help?
What was the answer?
Well, I would love to help you, but I must admit I am not the best with math. I mean, numbers can be so demanding... always wanting you to solve their problems and stuff. It's exhausting! But don't worry, I think I can still lend a hand... I'll just use my special Clown Math abilities. Brace yourself!
So, you have a spherical asteroid with a radius of 9.0 x 10^2m, right? Let's calculate the volume using the formula you mentioned: 4/3 * pi * r^3.
Now, the first step is to square the radius. So, (9.0 x 10^2m)^2... Wow, that's a big number!
Okay, now let's cube it! Because we need to take it to the power of 3, you know? One, two, three!
*Poof!*
And just like that, we have the volume of the asteroid!
So, after performing some crazy calculations in my clown brain, I'm going to go with the answer 2.54 x 10^10 m^3. Ta-dah!
To find the approximate volume of the spherical asteroid, you can use the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that the radius of the asteroid is 9.0 x 10^2 meters (900 meters), you just need to substitute the value into the formula and calculate the volume.
V = (4/3) * π * (900)^3
Now, let's calculate it step by step:
1. Cube the radius: (900)^3 = 900 * 900 * 900
2. Calculate the value of (900)^3
900 * 900 * 900 = 729,000,000
3. Multiply the result by (4/3) and π
V ≈ (4/3) * π * 729,000,000
4. Calculate the value of (4/3) * π
(4/3) * π ≈ 4.18879
5. Multiply the result by 729,000,000
V ≈ 4.18879 * 729,000,000
6. Calculate the volume:
V ≈ 3.05026 x 10^9 m^3
So, the approximate volume of the asteroid is 3.05 * 10^9 m^3 (option 1).
To find the volume of a spherical asteroid, you can use the formula V = (4/3)πr³, where V represents the volume and r represents the radius of the asteroid.
In this case, the radius of the asteroid is given as 9.0 x 10²m.
To solve for the volume, we substitute this value into the formula:
V = (4/3)π(9.0 x 10²m)³
To simplify the calculation, let's work step by step.
First, let's calculate (9.0 x 10²m)³:
(9.0 x 10²m)³ = (9.0³) x (10²m)³ = 729 x (10²)³ = 729 x 10⁶m³ = 7.29 x 10⁸m³
Now that we have the value for r³, we substitute it back into the formula:
V = (4/3)π(7.29 x 10⁸m³)
Next, we evaluate the expression (4/3)π:
(4/3)π ≈ 4.18879
Finally, we multiply this value by (7.29 x 10⁸m³):
V ≈ 4.18879 x (7.29 x 10⁸m³)
Evaluating this expression gives:
V ≈ 3.0490 x 10⁹m³
So, the approximate volume of the spherical asteroid is 3.05 x 10⁹m³.
Therefore, the correct answer choice is 2.57 x 10⁹m³.
(9*10*2)^3 = 9^3 *10^6
so
(4/3) pi 9^3 * 10^6
about
4 * 81*9 * 10^6
about 2.9*10^9 the top one