Anne made a semi-circular table cloth. The diameter of the table cloth was 42 cm. She binded the edge of the…

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Anne made a semi-circular table cloth. The diameter of the table cloth was 42 cm. She binded the edge of the table cloth with a ribbon. What was the length of the ribbon used?

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10. Anne made a semi-circular table cloth. The diameter of the table cloth was 42 cm. She binded the edge of the table cloth with a ribbon. What was the length of the ribbon used?

Identify the components of the edge of a semi-circular table cloth.
The edge consists of two parts:
- The curved part, which is half the circumference of a full circle.
- The straight part, which is the diameter of the semi-circle.
Calculate the length of the curved part.
The circumference of a full circle is given by $C = \pi d$ .
For a semi-circle, the curved length is $\frac{1}{2} \pi d$ .
Given diameter $d = 42$ cm. We will use $\pi = \frac{22}{7}$ .
$\text{Curved length} = \frac{1}{2} \times \frac{22}{7} \times 42$ $\text{Curved length} = \frac{1}{2} \times 22 \times 6$ $\text{Curved length} = 11 \times 6 = 66 \text{ cm}$
Calculate the total length of the ribbon.
Total ribbon length = Curved length + Diameter
$\text{Total ribbon length} = 66 \text{ cm} + 42 \text{ cm}$ $\text{Total ribbon length} = 108 \text{ cm}$
Compare with the given options.
The calculated length is 108 cm, which matches option B.

The final answer is $\boxed{\text{B. 108 cm}}$ .

11. A milk company sells yoghurt in cylindrical cups. Each cup has a diameter of 7 cm and a height of 10 cm. The company sold 385 litres of yoghurt. How many cups of yoghurt were sold?
Calculate the radius of a single cup.
Diameter $d = 7$ cm.
Radius $r = \frac{d}{2} = \frac{7}{2} = 3.5 \text{ cm}$ .
Calculate the volume of one cylindrical cup.
The formula for the volume of a cylinder is $V = \pi r^2 h$ . We will use $\pi = \frac{22}{7}$ .
$V_{\text{cup}} = \frac{22}{7} \times (3.5)^2 \times 10$ $V_{\text{cup}} = \frac{22}{7} \times (3.5 \times 3.5) \times 10$ $V_{\text{cup}} = \frac{22}{7} \times 12.25 \times 10$ $V_{\text{cup}} = 22 \times 1.75 \times 10$ $V_{\text{cup}} = 38.5 \times 10 = 385 \text{ cm}^3$
Convert the total volume of yoghurt sold from litres to cubic centimeters.
Given total volume sold = 385 litres.
Since $1 \text{ litre} = 1000 \text{ cm}^3$ :
$\text{Total volume sold} = 385 \times 1000 = 385000 \text{ cm}^3$
Calculate the number of cups sold.
$\text{Number of cups} = \frac{\text{Total volume sold}}{\text{Volume of one cup}}$ $\text{Number of cups} = \frac{385000 \text{ cm}^3}{385 \text{ cm}^3/\text{cup}}$ $\text{Number of cups} = 1000$
Compare with the given options.
The calculated number of cups is 1000, which matches option C.

The final answer is $\boxed{\text{C. 1000}}$ .

12. Nyaboke walked from her home to the market. She walked at a speed of 4 km/h and took 30 minutes to reach the market. On her way back, she took 40 minutes to reach home. What was Nyaboke's speed on her way back?
Calculate the distance from home to the market.
Speed to market $S_1 = 4$ km/h.
Time to market $T_1 = 30$ minutes. Convert minutes to hours: $30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours}$ .
Distance $D = S_1 \times T_1$
$D = 4 \text{ km/h} \times 0.5 \text{ h}$ $D = 2 \text{ km}$
Calculate Nyaboke's speed on her way back.
The distance back home is the same, $D = 2$ km.
Time taken on the way back $T_2 = 40$ minutes. Convert minutes to hours: $40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}$ .
Speed on the way back $S_2 = \frac{D}{T_2}$
$S_2 = \frac{2 \text{ km}}{\frac{2}{3} \text{ h}}$ $S_2 = 2 \times \frac{3}{2} \text{ km/h}$ $S_2 = 3 \text{ km/h}$
Compare with the given options.
The calculated speed is 3 km/h, which matches option B.

The final answer is $\boxed{\text{B. 3 km/h}}$ .

13. Mueni measured the temperature of a liquid as $48^\circ$ C. Which of the following calculations gives the correct temperature in Kelvin?
Recall the formula for converting temperature from Celsius to Kelvin.
The formula to convert a temperature in degrees Celsius ( $^\circ$ C) to Kelvin (K) is:
$K = ^\circ C + 273.15$
Often, for simplicity or in certain contexts, 273 is used instead of 273.15.
Apply the formula to the given temperature.
Given temperature is $48^\circ$ C.
Using the approximation $K = ^\circ C + 273$ :
$K = 48 + 273$ $K = 273 + 48$
Compare with the given options.
Option A, $273 + 48$ , correctly represents this conversion.

The final answer is $\boxed{\text{A. } 273 + 48}$ .

Anne made a semi-circular table cloth. The diameter of the table cloth was 42 cm. She binded the edge of the table cloth with a ribbon. What was the length of the ribbon used?

Step-by-step solution

Identify the components of the edge of a semi-circular table cloth.

Calculate the length of the curved part.

Calculate the total length of the ribbon.

Compare with the given options.

Calculate the radius of a single cup.

Calculate the volume of one cylindrical cup.

Convert the total volume of yoghurt sold from litres to cubic centimeters.

Calculate the number of cups sold.

Compare with the given options.

Calculate the distance from home to the market.

Calculate Nyaboke's speed on her way back.

Compare with the given options.

Recall the formula for converting temperature from Celsius to Kelvin.

Apply the formula to the given temperature.

Compare with the given options.

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