The correct description of a sphere from the given options is:
- A sphere has a center.
A sphere is a three-dimensional shape where every point on its surface is equidistant from its center. It does not have faces, edges, or vertices.
Which of the following correctly describes a sphere?
1. A sphere has a face
2. A sphere has an edge
3. A sphere has a vertex
4, A sphere has a center
7 answers
Which of the following is true about the diameter of a sphere?
1. The diameter is the shortest length on a sphere
2. The diameter is not a chord
3. The diameter of a sphere passes through the center of the circle.
4. The diameter is 2.5 times the length of the radius
1. The diameter is the shortest length on a sphere
2. The diameter is not a chord
3. The diameter of a sphere passes through the center of the circle.
4. The diameter is 2.5 times the length of the radius
The statement that is true about the diameter of a sphere is:
- The diameter of a sphere passes through the center of the circle.
Additionally, I would like to clarify that:
- The diameter is the longest chord of a sphere, not the shortest (so statement 1 is false).
- The diameter is indeed a special type of chord (so statement 2 is false).
- The diameter is actually twice the length of the radius, not 2.5 times (so statement 4 is false).
Therefore, the correct answer is statement 3.
Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.
2,826pi in.^2
225pi in.^2
3,600pi in.^2
900pi in.^2
2,826pi in.^2
225pi in.^2
3,600pi in.^2
900pi in.^2
To find the surface area of a sphere, we use the formula:
\[ \text{Surface Area} = 4\pi r^2 \]
where \( r \) is the radius of the sphere. Given that the diameter of the sphere is 30 inches, we find the radius \( r \) as follows:
\[ r = \frac{\text{diameter}}{2} = \frac{30}{2} = 15 \text{ inches} \]
Now we can calculate the surface area:
\[ \text{Surface Area} = 4\pi (15)^2 \]
Calculating \( (15)^2 \):
\[ (15)^2 = 225 \]
Now substituting back into the surface area formula:
\[ \text{Surface Area} = 4\pi \times 225 = 900\pi \text{ in}^2 \]
Therefore, the surface area of the sphere is:
\[ \boxed{900\pi \text{ in}^2} \]
Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in.2 and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?
4 in. x 4 in. x 4 in.
1.2 in. x 1.2 in. x 1.2 in
4.5 in. x 4.5 in. x 4.5 in.
2.25 in. x 2.25 in. x 2.25 in.
4 in. x 4 in. x 4 in.
1.2 in. x 1.2 in. x 1.2 in
4.5 in. x 4.5 in. x 4.5 in.
2.25 in. x 2.25 in. x 2.25 in.
To find the dimensions of the cube box that can snugly fit the spherical soap with a surface area of 63.585 in², we first need to determine the radius of the sphere.
We use the surface area formula for a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Plugging in the surface area:
\[ 63.585 = 4 \times 3.14 \times r^2 \]
Now, calculating \( 4 \times 3.14 \):
\[ 4 \times 3.14 = 12.56 \]
Substituting this back into the equation:
\[ 63.585 = 12.56 r^2 \]
Next, we divide both sides by 12.56 to solve for \( r^2 \):
\[ r^2 = \frac{63.585}{12.56} \approx 5.06 \]
Now, taking the square root to find \( r \):
\[ r \approx \sqrt{5.06} \approx 2.25 \text{ in.} \]
Since the diameter of the sphere (which determines the size of the cube) is twice the radius, we calculate the diameter:
\[ \text{Diameter} = 2r \approx 2 \times 2.25 = 4.5 \text{ in.} \]
Since the cube must fit the sphere snugly, the dimensions of the cube box should also be equal to the diameter of the sphere.
Thus, the dimensions of the cube box should be:
\[ \boxed{4.5 \text{ in.} \times 4.5 \text{ in.} \times 4.5 \text{ in.}} \]