Which choice could you use to find the volume of the given sphere? (π = 3.14)
Responses
A V = 4(3.14)(4.5)3
V = 4(3.14) ( 4.5 ) 3
B V = 43
(3.14)(4.5)2
V = 4 3 (3.14) ( 4.5 ) 2
C V = 43
(3.14)(4.5)3
V = 4 3 (3.14) ( 4.5 ) 3
D V = (3.14)(4.5)3
C V = 4/3 (3.14) (4.5)^3
Determine the volume of the given sphere. (nearest tenth)
Responses
A 91.1 cubic units91.1 cubic units
B 286.1 cubic units286.1 cubic units
C 381.5 cubic units381.5 cubic units
D 401.6 cubic units
Raids= 4.5
To find the volume of the given sphere, we can use the formula V = (4/3)(π)(r^3), where r is the radius. In this case, the radius is 4.5.
Substituting the values into the formula, we get V = (4/3)(3.14)(4.5^3)
Calculating this, we get V ≈ 381.5 cubic units
Therefore, the correct choice is C: 381.5 cubic units.
A soccer field is a rectangle 90 meters wide and 120 meters long. The soccer team ran from one corner to the other corner, along the diagonal of the soccer field.
How far, in meters, did the players run?
To find the distance the players ran, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width and length of the soccer field form the legs of a right triangle, and the diagonal represents the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
diagonal^2 = width^2 + length^2
diagonal^2 = 90^2 + 120^2
diagonal^2 = 8100 + 14400
diagonal^2 = 22500
Taking the square root of both sides, we get:
diagonal ≈ √22500
diagonal ≈ 150 meters.
Therefore, the players ran approximately 150 meters.
To find the volume of a sphere, you can use the formula V = 4/3 * π * r^3, where π is approximately 3.14 and r is the radius of the sphere.
Now let's examine the given choices:
A) V = 4(3.14)(4.5)^3
This choice follows the correct formula for the volume of a sphere and substitutes the radius with 4.5. So this equation is the correct choice.
B) V = 4/3 * (3.14)(4.5)^2
This equation does not have the correct exponent for the radius. The radius should be cubed to find the volume of a sphere, not squared. Therefore, this choice is incorrect.
C) V = 4/3 * (3.14)(4.5)^3
This choice follows the correct formula for the volume of a sphere and substitutes the radius with 4.5. So this equation is also a correct choice.
D) V = (3.14)(4.5)^3
This equation does not have the correct coefficient for the volume of a sphere. The formula for the volume of a sphere should have 4/3 as the coefficient, not just 1. Therefore, this choice is incorrect.
So, the correct choices for finding the volume of the given sphere are options A and C.