Actual dimensions in ft of a hall if the dimensions of the scale model is 12 in -10 in -8 in and the scale factor is 124 is

The dimensions of the scale model is 12 in ×10 in ×8 in. Scale Factor =ScaleActual Scale Factor =124 124=ScaleActual 124=12 in ×10 in ×8 inActual Cross mul ...

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Standard VIII

Mathematics

Scale Factor

Actual dimens...

Question

Actual dimensions (in ft) of a hall if the dimensions of the scale model is $12 i n \times 10 i n \times 8 i n$ and the scale factor is $\frac{1}{24}$ is

24, 20, 16

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48, 40, 32

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6, 5, 4

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20, 24, 16

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Solution

The correct option is A $24, 20, 16$
The dimensions of the scale model is $12 i n \times 10 i n \times 8 i n$ .

Scale Factor $= \frac{S c a l e}{A c t u a l}$

Scale Factor $= \frac{1}{24}$

$\frac{1}{24} = \frac{S c a l e}{A c t u a l}$

$\frac{1}{24} = \frac{12 i n \times 10 i n \times 8 i n}{A c t u a l}$

Cross multiply.

$A c t u a l = (12 \times 24) i n \times (10 \times 24) i n \times (8 \times 24) i n$

$A c t u a l = 288 i n \times 240 i n \times 192 i n$

To convert the dimensions into feet, divide by $12$ .

$A c t u a l = \frac{288 i n \times 240 i n \times 192 i n}{12}$

$A c t u a l = 24 f t \times 20 f t \times 16 f t = 24, 20, 16$

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Actual dimensions (in ft) of a hall if the dimensions of the scale model is 12 in×10 in×8 in and the scale factor is 124 is

Actual dimensions (in ft) of a hall if the dimensions of the scale model is $12 i n \times 10 i n \times 8 i n$ and the scale factor is $\frac{1}{24}$ is