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$This top view of a swimming pool is drawn on 0.5-cm grid paper. The dimensions of the pool are 60m by 40m. Determine the scale factor of the reduction as a fraction or a decimal.$

$4$ . This top view of a swimming pool is drawn on $0.5-\mathrm{cm}$ grid paper. The dimensions of the pool are $60 \mathrm{~m}$ by $40 \mathrm{~m}$ . Determine the scale factor of the reduction as a fraction or a decimal.

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Math Problems

Grade 7

Scale drawings: scale factor word problems

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4

. This top view of a swimming pool is drawn on

0.5-\mathrm{cm}

grid paper. The dimensions of the pool are

60 \mathrm{~m}

40 \mathrm{~m}

. Determine the scale factor of the reduction as a fraction or a decimal.

Find Grid Squares: First, we need to find out how many grid squares represent the swimming pool's length and width on the paper.
Measure Length and Width: Assuming the length of the pool ( $60\,\text{m}$ ) is represented by ' $x$ ' grid squares and the width ( $40\,\text{m}$ ) by ' $y$ ' grid squares on the paper. We need to measure these on the grid paper.
Convert to Centimeters: Let's say we measured and found that the length is $12$ grid squares and the width is $8$ grid squares.
Calculate Scale Factor for Length: Now, we convert the real dimensions from meters to centimeters because the grid paper is measured in centimeters. $1\,\text{m} = 100\,\text{cm}$ , so $60\,\text{m} = 6000\,\text{cm}$ and $40\,\text{m} = 4000\,\text{cm}$ .
Calculate Scale Factor for Width: Next, we calculate the scale factor for the length and width separately. Scale factor for length = $(\text{number of grid squares} \times \text{size of each grid square}) / \text{real size in cm}$ . So for length, Scale factor = $(12 \times 0.5\,\text{cm}) / 6000\,\text{cm}$ .
Determine Overall Scale Factor: Perform the calculation for the length: Scale factor = $(6\,\text{cm}) / 6000\,\text{cm} = 1 / 1000$ .
Determine Overall Scale Factor: Perform the calculation for the length: Scale factor = $(6\,\text{cm}) / 6000\,\text{cm} = 1 / 1000$ . Now, do the same for the width: Scale factor = (number of grid squares $*$ size of each grid square) / real size in cm. So for width, Scale factor = ($8 $*$ $0$ . $5$ \,\text{cm}) / $4000$ \,\text{cm}$.
Determine Overall Scale Factor: Perform the calculation for the length: Scale factor = $(6\,\text{cm}) / 6000\,\text{cm} = 1 / 1000$ . Now, do the same for the width: Scale factor = (number of grid squares $*$ size of each grid square) / real size in cm. So for width, Scale factor = ($8 $*$ $0$ . $5$ \,\text{cm}) / $4000$ \,\text{cm}$. Perform the calculation for the width: Scale factor = $(4\,\text{cm}) / 4000\,\text{cm} = 1 / 1000$ .
Determine Overall Scale Factor: Perform the calculation for the length: Scale factor = $(6\,\text{cm}) / 6000\,\text{cm} = 1 / 1000$ . Now, do the same for the width: Scale factor = (number of grid squares $\times$ size of each grid square) / real size in cm. So for width, Scale factor = $(8 \times 0.5\,\text{cm}) / 4000\,\text{cm}$ . Perform the calculation for the width: Scale factor = $(4\,\text{cm}) / 4000\,\text{cm} = 1 / 1000$ . Since both the length and width have the same scale factor, we can conclude that the scale factor for the reduction of the swimming pool on the grid paper is $1 / 1000$ .