A flat rectangular roof measures 7.5m by 4m.1 2mm of rain falls on the roof.(1cm3 of water has a mass of 1 gram.)
The mass of water on the roof is:
7.5 x 4 x 0.002 x 1000 = 60 kg
60
The mass of water on the roof is 60 kg.
Well, that's a lot of rain! Let me calculate the amount of water that fell on the roof for you.
First, let's convert the dimensions of the roof to centimeters. The length is 7.5m, which is equal to 750cm, and the width is 4m, which is equal to 400cm.
To find the volume of the water that fell, we multiply the length, width, and height. The height is given as 1.2mm, which is equal to 0.12cm.
So, the volume of water that fell on the roof is 750cm * 400cm * 0.12cm, which is equal to 36,000 cubic centimeters.
Since you mentioned that 1cm3 of water has a mass of 1 gram, we can conclude that the amount of rain that fell on the roof has a mass of 36,000 grams.
Therefore, it rained 36,000 grams or 36 kilograms on the roof. That's enough rain to have a serious water fight or fill up a small swimming pool!
To find the total mass of rain that fell on the roof, we need to calculate the volume of the rainwater and then convert it to mass using the given conversion factor.
Step 1: Calculate the volume of rainwater in cubic meters.
Given: Length = 7.5m, Width = 4m, Rainfall = 12mm (or 0.012m)
The volume of water is given by:
Volume = Length x Width x Height
Volume = 7.5m x 4m x 0.012m = 0.36 cubic meters
Step 2: Convert the volume to grams using the conversion factor.
Given: 1 cm^3 of water = 1 gram
To convert the volume from cubic meters to cubic centimeters, we multiply by 1,000,000 (since 1 cubic meter = 1,000,000 cubic centimeters).
Volume in cm^3 = Volume in m^3 x 1,000,000
Volume in cm^3 = 0.36 x 1,000,000 = 360,000 cm^3
Therefore, the mass of the rainwater is equal to the volume in grams.
Mass of the rainwater = 360,000 grams
So, 360,000 grams (or 360 kilograms) of rain fell on the roof.