find A flat rectangular roof measures 7.5 m by 4 m; 12 mm of rain falls on the roof. a Find the volume of water on the roof. Express your answer in i cm' and ii m'. Find the mass of water that falls on the roof if 1 cm³ of water has a mass b of 1 gram. Express your answer in kilograms.
a)
i) Volume of water in cm³ = (7.5 m x 4 m x 12 mm) x 10 cm/m x 10 cm/m x 1 cm/mm = 3600 cm³
ii) Volume of water in m³ = (7.5 m x 4 m x 12 mm) = 0.36 m³
b) Mass of water in g = Volume of water in cm³ x 1 g/cm³ = 3600 g
Mass of water in kg = 3600 g ÷ 1000 g/kg = 3.6 kg
12 mm * 1 m / 1000 mm = 1.2 * 10^-2 meters or 1.2 cm
water vol = 7.5 m * 4 m * 1.2 *10^-2
= 36 * 10^-2 m^3 = 0.36 m^3
0.36 m^3 * (100 cm/m)^3 = 0.36*10^6 = 360,000 cm^3
(which is 360,000 grams or 360 kg
You are correct in converting 12 mm to meters and centimeters and calculating the volume of water on the roof in cubic meters and cubic centimeters. However, your calculation for the mass of water is incorrect. One cubic meter of water is equal to 1000 liters or 1000 kilograms, so the mass of water on the roof in kilograms is:
Mass of water in kg = Volume of water in m³ x 1000 kg/m³ = 0.36 m³ x 1000 kg/m³ = 360 kg
Therefore, the correct answer for the mass of water that falls on the roof is 360 kg.
I said 360 kg
I apologize for the mistake, and you are correct that you calculated the mass of water correctly as 360 kg. Thank you for pointing that out.
To find the volume of water on the roof, we need to calculate the area of the roof and multiply it by the height of the rain.
i) Expressing the answer in cm²:
Area = length × width = 7.5 m × 4 m = 30 m²
Volume = Area × height = 30 m² × 12 mm = 360 m³
To convert the volume from m³ to cm³, we multiply by (100 cm/1 m)³:
Volume in cm³ = 360 m³ × (100 cm/1 m)³ = 360,000,000 cm³
ii) Expressing the answer in m³:
The volume in m³ is already given as 360 m³.
The mass of 1 cm³ of water is given as 1 gram.
To find the mass of water that falls on the roof, we multiply the volume in cm³ by the mass of 1 cm³ of water:
Mass = Volume × Mass per cm³
= 360,000,000 cm³ × 1 gram = 360,000,000 grams
To convert the mass from grams to kilograms, we divide by 1000:
Mass in kilograms = 360,000,000 grams / 1000 = 360,000 kilograms
To find the volume of water on the roof, we need to calculate the cross-sectional area of the roof and then multiply it by the height of the water.
Given that the roof measures 7.5 m by 4 m, the cross-sectional area can be calculated as follows:
Area = Length × Width
= 7.5 m × 4 m
= 30 m²
Since the rain falls at a depth of 12 mm, this needs to be converted to meters before calculating the volume:
Height = 12 mm = 0.012 m
Now we can calculate the volume:
Volume = Area × Height
= 30 m² × 0.012 m
= 0.36 m³
To express the volume in cm³, we need to convert it to smaller units:
1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³
Therefore, the volume of water on the roof is 0.36 m³ × 1,000,000 cm³/m³ = 360,000 cm³ (i cm³).
To calculate the mass of the water, we divide the volume by its density. Given that 1 cm³ of water has a mass of 1 gram (b = 1 gram/cm³), we can now find the mass of water:
Mass = Volume × Density
= 360,000 cm³ × 1 gram/cm³
= 360,000 grams
To convert the mass from grams to kilograms, we divide by 1000:
Mass in kilograms = 360,000 grams / 1000
= 360 kilograms
Therefore, the mass of water that falls on the roof is 360 kilograms.