Question

The model of a building is constructed with the scale factor 1: 30.
(i) if the height of the model is 80 cm. Find the height of building in metres.
(ii) if actual volume of building is 27 m². Find the volume of the model.​

Answer 1

Answer:

Scale Factor = 1 : 30

Question (i):

Convert cm to m (actual):

1 cm = 30 cm

1 cm = 0.3 m

Find 80 cm:

80 cm = 0.3 x 80 = 24 m

Answer: The height of the building is 24 m

Question (ii):

Convert cm to m (actual)

1 cm = 30 cm

1 cm = 0.3 m

Find 1 m (actual):

0,3 m = 1 cm

1 m = 1 ÷ 0.3 = 10/3 cm

FInd 1 m³:

1m = 10/3 cm

(1m)³ = (10/3 cm)³

1 m³ = 1000/27 cm²

Find 27 m³:

27 m³ = 1000/27 x 27 = 1000 cm³

Convert 1000 cm³ to litres:

1 cm³ = 0.001 litres

1000 cm³ = 0.001 x 1000

1000 cm³ = 1 litres

Answer: The volume is 1 litres

thanks

Answer 2

Question :--- The model of a building is constructed with the scale factor 1: 30.

(i) if the height of the model is 80 cm. Find the height of building in metres.

(ii) if actual volume of building is 27 m³. Find the volume of the model.

Solution :---

Since scale Factor is 1:30 .

So ,

1 : 30 = 80 : x

or,

→ 1/30 = 80/x

→ x = 30*80

→ x = 2400 cm

Now, we know that,

→ 100cm = 1 m

So,

→ 2400 cm = 24m (Ans)

_____________________________

Now, volume is given as 27m³ ..

So,

→ (1/30)³ = (x/27)

→ 1/(30*30*30) = x/27

→ x = 27/30*30*30

→ x = 1/1000m³

Now, we know that,

→ 1m³ = 1000000cm³

so,

1/1000m³ = 1000000/1000 = 1000cm³ (Ans)

Hence, volume of model will be 1000cm³ ...