Question

1. which is the equation of the circle shown below?

a. $(x - 3)^2 + y^2 = 3$
b. $(x - 3)^2 + y^2 = 9$
c. $(x + 3)^2 + y^2 = 3$
d. $(x + 3)^2 + y^2 = 9$

1. a solid - glass sphere is cast with a radius of 30 cm. what is the volume, to the nearest whole number, of this sphere?

the formula for the volume of a sphere is $v=\frac{4}{3}pi r^{3}$
a. $3,768\\ cm^{3}$
b. $63,585\\ cm^{3}$
c. $113,040\\ cm^{3}$
d. $339,120\\ cm^{3}$

Explanation:

Step1: Recall the volume formula for a sphere

The volume \( V \) of a sphere is given by the formula \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere.

Step2: Substitute the given radius into the formula

We are given that the radius \( r = 30\space\text{cm} \). Substituting \( r = 30 \) into the formula, we get:
\( V=\frac{4}{3}\pi(30)^{3} \)
First, calculate \( 30^{3}=30\times30\times30 = 27000 \).
Then, \( \frac{4}{3}\times27000=4\times9000 = 36000 \).
So, \( V = 36000\pi \).

Step3: Calculate the numerical value

Using \( \pi\approx3.1416 \), we have \( V\approx36000\times3.1416 \).
\( 36000\times3.1416 = 113097.6 \approx113040 \) (when rounded to the nearest whole number, considering possible slight differences in \(\pi\) approximation used, but the closest option is \( 113040\space\text{cm}^3 \)).

Answer:

C. \( 113,040\space\text{cm}^3 \)