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Each cuboid in Figure 1 is made up of 4 identical wooden blocks. Each wooden block is a cuboid with square faces at its opposite ends. The 3 cuboids in Figure 1 are stacked together to form the cuboid in Figure 2. The length of the cuboid in figure 2 is
60cm. Find the volume of the cuboid in Figure 2.
Figure 1

B
Figure 2

$6$ . Each cuboid in Figure $1$ is made up of $4$ identical wooden blocks. Each wooden block is a cuboid with square faces at its opposite ends. The $3$ cuboids in Figure $1$ are stacked together to form the cuboid in Figure $2$ . The length of the cuboid in figure $2$ is $60 \mathrm{~cm}$ . Find the volume of the cuboid in Figure $2$ . $\newline$ Figure $1$ $\newline$ $B$ $\newline$ Figure $2$

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Scale drawings: word problems

Full solution

Q.

6

. Each cuboid in Figure

1

is made up of

4

identical wooden blocks. Each wooden block is a cuboid with square faces at its opposite ends. The

3

cuboids in Figure

1

are stacked together to form the cuboid in Figure

2

. The length of the cuboid in figure

2

is

60 \mathrm{~cm}

. Find the volume of the cuboid in Figure

2

.

\newline

Figure

1

\newline

B

\newline

Figure

2

Determine Wooden Block Length: Step $1$ : Determine the length of one wooden block. Since $3$ cuboids make up the length of the cuboid in Figure $2$ , and each cuboid is made of $4$ wooden blocks, the length of one wooden block is $60\,\text{cm}$ divided by $3$ . Calculation: $60\,\text{cm} / 3 = 20\,\text{cm}$ .
Calculate Block Volume: Step $2$ : Calculate the volume of one wooden block. $\newline$ The wooden block is a cuboid with square faces, so its width and height are the same as its length. $\newline$ Calculation: Volume = $\text{length} \times \text{width} \times \text{height} = 20\,\text{cm} \times 20\,\text{cm} \times 20\,\text{cm} = 8000\,\text{cm}^3$ .
Calculate Cuboid Volume: Step $3$ : Calculate the volume of the cuboid in Figure $2$ . $\newline$ Since there are $12$ identical wooden blocks, multiply the volume of one block by $12$ . $\newline$ Calculation: Total volume = $8000\,\text{cm}^3 \times 12 = 96000\,\text{cm}^3$ .

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