Question

1 here is a scale drawing of a swimming pool where 1 cm represents 1 m. a. how long and how wide is the actual swimming pool? b. will a scale drawing where 1 cm represents 2 m be larger or smaller than this drawing? c. make a scale drawing of the swimming pool where 1 cm represents 2 m.

Explanation:

Part (a)

To determine the actual length and width, we first need to measure the length and width of the scale drawing (assuming we can visually estimate or measure it). Let's assume the scale drawing of the pool has a length of, say, 5 cm and a width of 3 cm (since the actual measurement from the image isn't provided, we'll use sample values for demonstration; in a real scenario, you'd measure the drawing).

Step 1: Determine the scale factor

The scale is \( 1 \, \text{cm} = 1 \, \text{m} \), so the scale factor is \( 1 \, \text{m/cm} \).

Step 2: Calculate actual length

If the drawing length is \( 5 \, \text{cm} \), then actual length \( = 5 \, \text{cm} \times 1 \, \text{m/cm} = 5 \, \text{m} \).

Step 3: Calculate actual width

If the drawing width is \( 3 \, \text{cm} \), then actual width \( = 3 \, \text{cm} \times 1 \, \text{m/cm} = 3 \, \text{m} \).

Part (b)

Step 1: Understand scale relationships

A larger scale (e.g., \( 1 \, \text{cm} = 1 \, \text{m} \)) means more real-world units are represented per centimeter. A smaller scale (e.g., \( 1 \, \text{cm} = 2 \, \text{m} \)) means fewer real-world units are represented per centimeter.

Step 2: Compare the two scales

For the same actual pool, a scale of \( 1 \, \text{cm} = 2 \, \text{m} \) will require fewer centimeters to represent the same length/width than \( 1 \, \text{cm} = 1 \, \text{m} \). Thus, the drawing with \( 1 \, \text{cm} = 2 \, \text{m} \) will be smaller than the original drawing.

Part (c)

Step 1: Use the new scale

The new scale is \( 1 \, \text{cm} = 2 \, \text{m} \). From part (a), the actual length is \( 5 \, \text{m} \) and width is \( 3 \, \text{m} \).

Step 2: Calculate drawing dimensions

• Drawing length: \( \frac{\text{Actual length}}{\text{Scale factor}} = \frac{5 \, \text{m}}{2 \, \text{m/cm}} = 2.5 \, \text{cm} \)
• Drawing width: \( \frac{\text{Actual width}}{\text{Scale factor}} = \frac{3 \, \text{m}}{2 \, \text{m/cm}} = 1.5 \, \text{cm} \)

Step 3: Draw the rectangle

Draw a rectangle with length \( 2.5 \, \text{cm} \) and width \( 1.5 \, \text{cm} \) to represent the pool at the new scale.

Final Answers

a. (Using sample measurements) Actual length: \( \boldsymbol{5 \, \text{m}} \), Actual width: \( \boldsymbol{3 \, \text{m}} \) (adjust based on actual drawing measurements).
b. The drawing will be \( \boldsymbol{\text{smaller}} \).
c. Draw a rectangle with length \( 2.5 \, \text{cm} \) and width \( 1.5 \, \text{cm} \) (adjust based on actual part (a) values).

Answer:

Part (a)

To determine the actual length and width, we first need to measure the length and width of the scale drawing (assuming we can visually estimate or measure it). Let's assume the scale drawing of the pool has a length of, say, 5 cm and a width of 3 cm (since the actual measurement from the image isn't provided, we'll use sample values for demonstration; in a real scenario, you'd measure the drawing).

Step 1: Determine the scale factor

The scale is \( 1 \, \text{cm} = 1 \, \text{m} \), so the scale factor is \( 1 \, \text{m/cm} \).

Step 2: Calculate actual length

If the drawing length is \( 5 \, \text{cm} \), then actual length \( = 5 \, \text{cm} \times 1 \, \text{m/cm} = 5 \, \text{m} \).

Step 3: Calculate actual width

If the drawing width is \( 3 \, \text{cm} \), then actual width \( = 3 \, \text{cm} \times 1 \, \text{m/cm} = 3 \, \text{m} \).

Part (b)

Step 1: Understand scale relationships

A larger scale (e.g., \( 1 \, \text{cm} = 1 \, \text{m} \)) means more real-world units are represented per centimeter. A smaller scale (e.g., \( 1 \, \text{cm} = 2 \, \text{m} \)) means fewer real-world units are represented per centimeter.

Step 2: Compare the two scales

For the same actual pool, a scale of \( 1 \, \text{cm} = 2 \, \text{m} \) will require fewer centimeters to represent the same length/width than \( 1 \, \text{cm} = 1 \, \text{m} \). Thus, the drawing with \( 1 \, \text{cm} = 2 \, \text{m} \) will be smaller than the original drawing.

Part (c)

Step 1: Use the new scale

The new scale is \( 1 \, \text{cm} = 2 \, \text{m} \). From part (a), the actual length is \( 5 \, \text{m} \) and width is \( 3 \, \text{m} \).

Step 2: Calculate drawing dimensions

• Drawing length: \( \frac{\text{Actual length}}{\text{Scale factor}} = \frac{5 \, \text{m}}{2 \, \text{m/cm}} = 2.5 \, \text{cm} \)
• Drawing width: \( \frac{\text{Actual width}}{\text{Scale factor}} = \frac{3 \, \text{m}}{2 \, \text{m/cm}} = 1.5 \, \text{cm} \)

Step 3: Draw the rectangle

Draw a rectangle with length \( 2.5 \, \text{cm} \) and width \( 1.5 \, \text{cm} \) to represent the pool at the new scale.

Final Answers

a. (Using sample measurements) Actual length: \( \boldsymbol{5 \, \text{m}} \), Actual width: \( \boldsymbol{3 \, \text{m}} \) (adjust based on actual drawing measurements).
b. The drawing will be \( \boldsymbol{\text{smaller}} \).
c. Draw a rectangle with length \( 2.5 \, \text{cm} \) and width \( 1.5 \, \text{cm} \) (adjust based on actual part (a) values).