An inverted regular square pyramid has an altitude of 12m...

An inverted regular square pyramid has an altitude of 12m and with top edge of 3m is fully-filled with water. 4. What is the volume of the water in m³? A portion of water is to be removed so that water will be 7m deep. 5. What is the area at the surface of the water when it is 7m deep? 6. How much water is to be removed so that water is 7m deep? 7. How much water retained when it is 7m deep?

Transcript

00:01 In this question we are given the height of the inverted parameter which is 12 meters and the edge is equals to which is represented by a is equal to 3 meters and height is represented by small edge so in the first part of the first question which is represented by number 4 we have to find the volume of the water.

00:27 So for finding the volume of the water we will find the volume of pyramid which is equal to a squared multiplied by h divided by 3 so it will be equals to 3 square multiplied by h which is 12 divided by 3 so it comes out to be 36 mccube so this is the volume of the pyramid so the volume of water will be equals to 36 meter cube because it is totally filled by water.

01:07 Now the portion of a water is removed now its depth is 7 meters.

01:16 Now in the fifth part we have to find the area at the surface of the water.

01:22 So the new height of the water which is represented by h -dash is 7 meters.

01:33 So the new base edge which is represented by a dash will be equals to edge multiplied by a divided by h so it will be equals to 7 multiplied by 3 divided by 12 so it will be equals to 1 .75 meters this is a new edge so area at the surface of water when the depth is equals to 7 meters will be equals to the edge square which is 1 .75 whole square so it will be 3 .0625 meter square now moving on to the next part firstly wills of the 7 because in the 6 part we will use the part number 7 so when the water remained is is having a depth of 7 meters so the volume of water remaining will be calculated by calculating the volume of water it will be equals to a dash whole square multiplied by height divided by 3 so it will be 1 .75 whole square multiplied by 7 divided by 3 so it will come out to be 7 .145 meter cube.

03:22 Now moving on to the 6 part now...

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