1. What is the length of the radius of a sphere with a diameter of 12 cm?(1 point)

Question

cm

2. Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.(1 point)
The surface area is in.^2

3. Find the surface area of a sphere with a radius of 3.6 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary.(1 point)
The surface area is ft.^2

4. A cube box is 20 cm×20 cm×20 cm
20

cm
×
20


cm
×
20

cm
. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.(1 point)
cm^2

5. A rectangular box is 12 in. × 14 in. × 18 in.
12

in
.

×

14

in
.

×

18

in
.
What is the surface area of the largest size sphere that could fit in this box? Leave your answer in terms of pi.(1 point)
in^2

Answer 1

Here are the answers to each of your questions:

1. What is the length of the radius of a sphere with a diameter of 12 cm?

   • The radius is half of the diameter.
   • Radius = Diameter / 2 = 12 cm / 2 = 6 cm

2. Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.

   • The formula for the surface area of a sphere is \( S = 4\pi r^2 \).
   • First, find the radius: \( r = \text{Diameter} / 2 = 40 \text{ in} / 2 = 20 \text{ in} \).
   • Surface area \( S = 4\pi (20 \text{ in})^2 = 4\pi (400) = 1600\pi \).
   • The surface area is 1600π in².

3. Find the surface area of a sphere with a radius of 3.6 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary.

   • Using the formula \( S = 4\pi r^2 \):
   • Surface area \( S = 4 \cdot 3.14 \cdot (3.6 \text{ ft})^2 = 4 \cdot 3.14 \cdot 12.96 \).
   • Calculating that: \( 4 \cdot 3.14 = 12.56 \).
   • Then \( 12.56 \cdot 12.96 \approx 162.74 \) ft².
   • The surface area is 162.74 ft².

4. What is the surface area of the largest size sphere that can fit in a box measuring 20 cm × 20 cm × 20 cm? Leave your answer in terms of pi.

   • The largest sphere that can fit inside the cube will have a diameter equal to the side length of the cube.
   • Diameter = 20 cm ⇒ Radius = 10 cm.
   • Using \( S = 4\pi r^2 \):
   • Surface area \( S = 4\pi (10 \text{ cm})^2 = 4\pi (100) = 400\pi \).
   • The surface area is 400π cm².

5. What is the surface area of the largest size sphere that could fit in a box measuring 12 in. × 14 in. × 18 in.? Leave your answer in terms of pi.

   • The largest sphere that can fit in the rectangular box will have a diameter equal to the smallest dimension of the box.
   • The smallest dimension is 12 in. ⇒ Radius = 6 in.
   • Using the formula \( S = 4\pi r^2 \):
   • Surface area \( S = 4\pi (6 \text{ in})^2 = 4\pi (36) = 144\pi \).
   • The surface area is 144π in².

Here is a summary of the answers:

1. 6 cm
2. 1600π in²
3. 162.74 ft²
4. 400π cm²
5. 144π in²

Answer 2

1. Which of the following correctly describes a sphere?(1 point)
Responses

A sphere has a vertex.
A sphere has a vertex.

A sphere has a face.
A sphere has a face.

A sphere has a center.
A sphere has a center.

A sphere has an edge.

2. Which of the following is true about the diameter of a sphere?(1 point)
Responses

The diameter of a sphere passes through the center of the circle.
The diameter of a sphere passes through the center of the circle.

The diameter is not a chord.
The diameter is not a chord.

The diameter is 2.5 times the length of the radius.
The diameter is 2.5 times the length of the radius.

The diameter is the shortest length on a sphere.

3. Use the formula for the surface area of a sphere to find the surface area of a basketball that has a diameter of 9.2 inches. Use 3.14 pi and round your answer to the nearest hundredth, if necessary.(1 point)
Responses

66.44 in.^2

1,063.08 in.^2

84.64 in.^2

265.77 in.^2

Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.(1 point)
Responses

3,600π in.^2

2,826π in.^2

225π in.^2

900π in.^2

5. Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in.^2
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?(1 point)
Responses

4.5 in. × 4.5 in. × 4.5 in.
4.5

in.

×

4.5

in.

×

4.5

in
.
4.5 inches times 4.5 inches times 4.5 inches

4 in.× 4 in.× 4 in.
4

in.
×

4

in.
×

4

in
.
4 inches times 4 inches times 4 inches

2.25 in. × 2.25 in. × 2.25 in.
2.25

in.

×

2.25

in.

×

2.25

in
.
2.25 inches times 2.25 inches times 2.25 inches

1.2 in. × 1.2 in. × 1.2 in.

Answer 3

Here are the answers to your questions:

1. Which of the following correctly describes a sphere?

   • The correct response is: A sphere has a center.
     (A sphere does not have a vertex, face, or edge.)

2. Which of the following is true about the diameter of a sphere?

   • The correct response is: The diameter of a sphere passes through the center of the circle.
     (The diameter is a special type of chord, it is not the shortest length on a sphere, nor is it 2.5 times the length of the radius; the diameter is exactly 2 times the radius.)

3. Use the formula for the surface area of a sphere to find the surface area of a basketball that has a diameter of 9.2 inches. Use 3.14 for pi and round your answer to the nearest hundredth, if necessary.

   • First, find the radius:
     • Radius = Diameter / 2 = 9.2 in / 2 = 4.6 in.
   • Surface area \( S = 4\pi r^2 = 4 \cdot 3.14 \cdot (4.6)^2 \).
   • Calculate \( (4.6)^2 = 21.16 \).
   • Now \( S = 4 \cdot 3.14 \cdot 21.16 = 4 \cdot 66.47584 = 265.90336 \).
   • Rounding to the nearest hundredth gives: 265.90 in².
   • Since the closest option is 265.77 in², that is the correct response in this context.

4. Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.

   • First, find the radius:
     • Radius = Diameter / 2 = 30 in / 2 = 15 in.
   • Surface area \( S = 4\pi r^2 = 4\pi (15)^2 = 4\pi (225) = 900\pi \).
   • The correct response is: 900π in².

5. Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in² 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?

   • First, we need to find the radius from the surface area:
   • The surface area \( S = 4\pi r^2 \) ⇒ \( 63.585 = 4 \cdot 3.14 \cdot r^2 \).
   • Calculate \( 4 \cdot 3.14 = 12.56 \), then:
   • \( 63.585 = 12.56 \cdot r^2 \)
   • Dividing both sides by 12.56 gives us \( r^2 = 63.585 / 12.56 \approx 5.06 \).
   • Taking the square root to find the radius: \( r \approx 2.25 \) in.
   • Since the largest sphere that can fit in the cube has a diameter of \( 2 \cdot 2.25 = 4.5 \) in, the dimensions of the cube box should be:
   • 4.5 in. × 4.5 in. × 4.5 in.

Here’s a summary of the answers:

1. A sphere has a center.
2. The diameter of a sphere passes through the center of the circle.
3. 265.77 in² (or 265.90 in² if we round correctly)
4. 900π in².
5. 4.5 in. × 4.5 in. × 4.5 in.

Answer 4

3. for PRACTICE is 162.78

all for the quick check is PERFECT! same with 1 2 4 5 in practice.

Answer 5

Great to hear that you found the answers for the quick check to be perfect! Thank you for the update on question 3 in your practice; if the calculated surface area for the basketball is approximately 162.78 in², that aligns more closely with your rounding approach.

To clarify, for the basketball with a diameter of 9.2 inches:

1. Calculate the radius: \[ \text{Radius} = \frac{9.2}{2} = 4.6 \text{ in}\]
2. Use the surface area formula: \[ S = 4\pi r^2 = 4 \cdot 3.14 \cdot (4.6)^2 \] \[ (4.6)^2 \approx 21.16 \] \[ S \approx 4 \cdot 3.14 \cdot 21.16 \approx 4 \cdot 66.4816 \approx 265.93 \text{ in²} \]

However, if you’re using a different calculation or rounding method that gives 162.78 in², I'd recommend double-checking the surface area formula and calculations.

If you need further clarification or assistance on any other topics, feel free to ask!