Question

c) calculate the total price with tax.

1. convert the following measurements.

a) 312 cm = ______ m
b) 22.5 km = ______ m
c) 456 mm = ______ cm
d) 0.68 m = ______ cm

1. calculate the circumference of each circle. round to 2 decimal places.

a)
b)

1. calculate the area of each circle. round to 2 decimal places.

a)
b)

1. calculate the volume of each shape. round to 2 decimal places.

a)
b)

Explanation:

⚡ Using: Parts of a Circle (radius, diameter, chord, tangent, secant, arc, sector) · 🆕 New: Metric Conversions and Geometric Formulas
Converting units and calculating circle/cylinder properties

Step 1: Convert the measurements (Question 8)

To convert metric units, we use the following relationships:

• \( 1\text{ m} = 100\text{ cm} \)
• \( 1\text{ km} = 1000\text{ m} \)
• \( 1\text{ cm} = 10\text{ mm} \)

a) Convert \( 312\text{ cm} \) to \( \text{m} \):
\[ 312 \div 100 = 3.12\text{ m} \]

b) Convert \( 22.5\text{ km} \) to \( \text{m} \):
\[ 22.5 \times 1000 = 22,500\text{ m} \]

c) Convert \( 456\text{ mm} \) to \( \text{cm} \):
\[ 456 \div 10 = 45.6\text{ cm} \]

d) Convert \( 0.68\text{ m} \) to \( \text{cm} \):
\[ 0.68 \times 100 = 68\text{ cm} \]

---

Step 2: Calculate the circumference of each circle (Question 9)

The formula for the circumference of a circle given its diameter \( d \) is:
\[ C = \pi d \]

a) Circle with diameter \( d = 5\text{ cm} \):
\[ C = \pi \times 5 \approx 15.71\text{ cm} \]

b) Circle with diameter \( d = 8.36\text{ m} \):
\[ C = \pi \times 8.36 \approx 26.26\text{ m} \]

---

Step 3: Calculate the area of each circle (Question 10)

The formula for the area of a circle is:
\[ A = \pi r^2 \]
where \( r \) is the radius. Since the diagrams show the diameter \( d \), we first find the radius using \( r = \frac{d}{2} \).

a) Circle with diameter \( d = 5\text{ cm} \):

• Radius: \( r = \frac{5}{2} = 2.5\text{ cm} \)
• Area:

\[ A = \pi \times (2.5)^2 = 6.25\pi \approx 19.63\text{ cm}^2 \]

b) Circle with diameter \( d = 8.36\text{ m} \):

• Radius: \( r = \frac{8.36}{2} = 4.18\text{ m} \)
• Area:

\[ A = \pi \times (4.18)^2 = 17.4724\pi \approx 54.89\text{ m}^2 \]

---

Step 4: Calculate the volume of each cylinder (Question 11)

The formula for the volume of a cylinder is:
\[ V = \pi r^2 h \]
where \( r \) is the radius of the circular base and \( h \) is the height. The diagrams show the diameter of the circular top and the height of the cylinder.

a) Cylinder with diameter \( d = 4\text{ m} \) and height \( h = 10\text{ m} \):

• Radius: \( r = \frac{4}{2} = 2\text{ m} \)
• Volume:

\[ V = \pi \times 2^2 \times 10 = 40\pi \approx 125.66\text{ m}^3 \]

b) Cylinder with diameter \( d = 7\text{ m} \) and height \( h = 11\text{ m} \):

• Radius: \( r = \frac{7}{2} = 3.5\text{ m} \)
• Volume:

\[ V = \pi \times (3.5)^2 \times 11 = 134.75\pi \approx 423.33\text{ m}^3 \]

---

Answer:

8. Measurement Conversions

• a) \( 3.12\text{ m} \)
• b) \( 22,500\text{ m} \)
• c) \( 45.6\text{ cm} \)
• d) \( 68\text{ cm} \)

9. Circumference

• a) \( 15.71\text{ cm} \)
• b) \( 26.26\text{ m} \)

10. Area

• a) \( 19.63\text{ cm}^2 \)
• b) \( 54.89\text{ m}^2 \)

11. Volume

• a) \( 125.66\text{ m}^3 \)
• b) \( 423.33\text{ m}^3 \)