A sphere with a diameter of 13 millimeters

Question

Which measurements is the closest to the volume of the marble in cubic millimeters?

answers:

1,150 mm^3

836 mm^3

6,902 mm^ 3

9,203 mm^3

Answer 1

To find the volume of a sphere, we use the formula:

$$V=\frac{4}{3}\pi r^3$$

where $V$ is the volume and $r$ is the radius of the sphere.

Given that the diameter of the sphere is 13 millimeters, we can find the radius by dividing the diameter by 2:

$$r=\frac{13}{2}=6.5\text{ mm}$$

Now, we can substitute the radius into the volume formula:

$$V=\frac{4}{3}\pi (6.5{)}^3$$

Calculating $(6.5{)}^3$:

$$(6.5{)}^3=6.5\times 6.5\times 6.5=274.625$$

Now substituting back into the volume formula:

$$V=\frac{4}{3}\pi (274.625)$$

Now, calculating $\frac{4}{3}\times 274.625$:

$$\frac{4}{3}\times 274.625\approx 366.167$$

Now, calculating the volume with $\pi$:

$$V\approx 366.167\times 3.14159\approx 1,150.56{\text{ mm}}^3$$

Thus, the closest measurement to the volume of the marble in cubic millimeters is:

1,150 mm³