Questions: Consider the following figure. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference (in cm ) of the figure. exact cm approximation cm (b) Find the area (in cm^2 ) of the figure. exact cm^2 approximation cm^2

Consider the following figure. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference (in cm ) of the figure. exact cm approximation cm (b) Find the area (in cm^2 ) of the figure. exact cm^2 approximation cm^2
Transcript text: Consider the following figure. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference (in cm ) of the figure. exact $\square$ cm approximation $\square$ cm (b) Find the area (in $\mathrm{cm}^{2}$ ) of the figure. exact $\square$ $\mathrm{cm}^{2}$ approximation $\square$ $\mathrm{cm}^{2}$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the given information

The radius of the circle is given as 8 cm.

Step 2: Calculate the exact circumference

The formula for the circumference of a circle is \( C = 2\pi r \). Substitute \( r = 8 \) cm: \[ C = 2\pi \times 8 = 16\pi \text{ cm} \]

Step 3: Calculate the approximate circumference

Use the approximation \( \pi \approx 3.14 \): \[ C \approx 16 \times 3.14 = 50.24 \text{ cm} \]

Step 4: Calculate the exact area

The formula for the area of a circle is \( A = \pi r^2 \). Substitute \( r = 8 \) cm: \[ A = \pi \times 8^2 = 64\pi \text{ cm}^2 \]

Step 5: Calculate the approximate area

Use the approximation \( \pi \approx 3.14 \): \[ A \approx 64 \times 3.14 = 200.96 \text{ cm}^2 \]

Final Answer

(a) Find the circumference (in cm) of the figure.

  • Exact: \( 16\pi \) cm
  • Approximation: 50.24 cm

(b) Find the area (in cm\(^2\)) of the figure.

  • Exact: \( 64\pi \) cm\(^2\)
  • Approximation: 200.96 cm\(^2\)
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A U.S. manager is tasked with choosing the next foreign market in which to establish a manufacturing facility. The manager needs to choose between a mark that allows for the firm to derive income from its facility and one where facilities are partially owned by the government. Which factor is the manager considering? a. democracy b. patents c. property rights d. common law
failedAnswered
Find the mode of the following number of times each machine in a car factory needed to be fixed within the last year. 2,5,6,12,14,12,6,2,5,3,14,5
failedAnswered
Place the following levels of organization from the most complex to the simplest level of organization. cellular level, tissue level, organ level, chemical level, organismal level chemical level, tissue level, cellular level, organismal level organ level chemical level, organ level, cellular level, tissue level, organismal level chemical level, cellular level, tissue level, organ level, organismal level
failedAnswered
Divide 12 3/4 by 8 =
failedAnswered
A 55.0 kilogram (kg) block of metal has an original temperature of 15.0°C and 0.45 J/g°C. What will be the final temperature of this metal if 75500 J of heat energy is absorbed by the metal?