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Question 1

A)Calculate the volume of a sphere that has a diameter of 7 inches. Use 3.14 for pi and round to the nearest tenth.(1 point)
$$ inches3
Question 2
A)Raphael wants to purchase an exercise ball. The dimensions state that the ball is 20 inches in diameter when at maximum capacity. How much air can the exercise ball hold when pumped to the maximum capacity? Calculate your answer using 3.14 for pi and round to the nearest tenth.(1 point)
$$ inches3
Question 3
A)
Use the image to answer the question.

A circle is traced along the circumference of a sphere at the center like a latitude. A dot is plotted at the center. The radius measures 2 centimeters.

Calculate the volume of the sphere using 3.14 for pi and round to the nearest tenth.

(1 point)
$$ cm3
Question 4
A)You buy a sphere-shaped piece of chocolate that has a creamy center. The chocolate piece measures 1 inch in diameter. How much creamy filling can fit inside the chocolate piece? Calculate your answer in terms of π and round to the nearest tenth.(1 point)
$$ inches3
Question 5
A)Calculate the volume of a sphere that has a diameter of 5 inches. Use 3.14 for pi and round to the nearest tenth.(1 point)
$$ inches3

1 answer

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

\[ V = \frac{4}{3} \pi r^3 \]

where \( r \) is the radius of the sphere.

Let's go through each question step-by-step:

Question 1

A) Diameter = 7 inches

First, we find the radius: \[ r = \frac{7}{2} = 3.5 \text{ inches} \]

Now we can calculate the volume: \[ V = \frac{4}{3} \times 3.14 \times (3.5)^3 \] Calculating \( (3.5)^3 = 42.875 \): \[ V = \frac{4}{3} \times 3.14 \times 42.875 \approx 179.594 \]

Rounding to the nearest tenth: \[ \text{Volume} \approx 179.6 \text{ inches}^3 \]

Question 2

A) Diameter = 20 inches

First, we find the radius: \[ r = \frac{20}{2} = 10 \text{ inches} \]

Now calculate the volume: \[ V = \frac{4}{3} \times 3.14 \times (10)^3 \] Calculating \( (10)^3 = 1000 \): \[ V = \frac{4}{3} \times 3.14 \times 1000 \approx 4186.6667 \]

Rounding to the nearest tenth: \[ \text{Volume} \approx 4186.7 \text{ inches}^3 \]

Question 3

A) Radius = 2 centimeters

Now we can calculate the volume: \[ V = \frac{4}{3} \times 3.14 \times (2)^3 \] Calculating \( (2)^3 = 8 \): \[ V = \frac{4}{3} \times 3.14 \times 8 \approx 33.5111 \]

Rounding to the nearest tenth: \[ \text{Volume} \approx 33.5 \text{ cm}^3 \]

Question 4

A) Diameter = 1 inch

First, we find the radius: \[ r = \frac{1}{2} = 0.5 \text{ inches} \]

Volume calculation: \[ V = \frac{4}{3} \times \pi \times (0.5)^3 \] Calculating \( (0.5)^3 = 0.125 \): \[ V = \frac{4}{3} \times \pi \times 0.125 = \frac{4}{3} \times 0.125 \pi \approx 0.1667 \pi \]

Using \( \pi \approx 3.14 \): \[ V \approx 0.1667 \times 3.14 \approx 0.5233 \]

Rounding to the nearest tenth: \[ \text{Volume} \approx 0.5 \text{ inches}^3 \]

Question 5

A) Diameter = 5 inches

First, we find the radius: \[ r = \frac{5}{2} = 2.5 \text{ inches} \]

Now calculate the volume: \[ V = \frac{4}{3} \times 3.14 \times (2.5)^3 \] Calculating \( (2.5)^3 = 15.625 \): \[ V = \frac{4}{3} \times 3.14 \times 15.625 \approx 65.45 \]

Rounding to the nearest tenth: \[ \text{Volume} \approx 65.5 \text{ inches}^3 \]

Summary of Answers:

  1. Question 1: 179.6 inches³
  2. Question 2: 4186.7 inches³
  3. Question 3: 33.5 cm³
  4. Question 4: 0.5 inches³
  5. Question 5: 65.5 inches³