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.
A. 3.05*10^9m^3
B. 1.95*10^11m^3
C. 3.05*10^9m^3
D. 1.13*10^4m^3
My Answer:
C. 3.05*10^9m^3
Correct,
Thank you!
You are welcome!
To find the volume of a spherical asteroid, we can use the formula:
Volume = (4/3) π r^3
where r is the radius of the asteroid.
Given that the radius is approximately 9.0 x 10^2m, we substitute this value into the formula:
Volume = (4/3) π (9.0 x 10^2)^3
Now, let's evaluate the expression:
Volume = (4/3) π (9.0 x 10^2)^3
Volume = (4/3) π (9.0^3) x (10^2)^3
Volume = (4/3) π (9.0^3) x (10^6)
Volume = (4/3) π (729) x (10^6)
Volume = 243π x (10^6)
Now, let's approximate the value of π to 3.14:
Volume ≈ 243 x 3.14 x (10^6)
Volume ≈ 763,620 x (10^6)
Volume ≈ 7.6362 x (10^5) x (10^6)
Using exponent addition:
Volume ≈ 7.6362 x 10^(5+6)
Volume ≈ 7.6362 x 10^11
So, the approximate volume of the asteroid is 7.6362 x 10^11 m^3.
Now, comparing the options:
A. 3.05*10^9 m^3
B. 1.95*10^11 m^3
C. 3.05*10^9 m^3
D. 1.13*10^4 m^3
The correct answer is B. 1.95*10^11m^3, which is the closest option to our calculated volume.