Question

Lianne drew a sphere with a radius of 7 in. She calculated its volume and wrote it below: (? π)(3) inches cubed. What value should be multiplied by π in the numerator to correctly show the volume of the sphere?

a) 7
b) 14
c) 21
d) 49

Answer 1

The value that should be multiplied by π in the numerator to show the correct volume of Lianne's sphere with a radius of 7 inches is 343, which is 7 to the third power, as per the formula V = (4/3) π r³.

Step-by-step explanation:

The question pertains to calculating the volume of a sphere with a given radius. The correct formula for the volume of a sphere is V = (4/3) π r³. Since Lianne's sphere has a radius of 7 inches, we use the formula to find that the volume is V = (4/3) π (7³), which simplifies to V = (4/3) π (343). Thus, when we multiply 343 by 4/3 we get 4/3 times 343 which equals 457.33. Therefore, the value that should be multiplied by π in the numerator to show the correct volume of the sphere is 343, multiplied by 4/3 to incorporate the complete formula.