SOLUTION: When she visited a spice market, Jessica was in awe of the beautiful colours and smells. She was also amazed at the ground spices that were sculpted into rectangular pyramids on t
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Question 1037643: When she visited a spice market, Jessica was in awe of the beautiful colours and smells. She was also amazed at the ground spices that were sculpted into rectangular pyramids on top of their boxes.
a. If the base of the pyramid was 12 cm by 8 cm and the mound of spice was 8 cm tall, what volume of spice was within the mound above the box (to the nearest cubic centimetre)?
b. Jessica bought 40 cm3 of this spice. Then, the shop owner recreated the pyramid with what was left. Given that the base has to stay the same dimensions how tall is the new pyramid? Round to two decimal places.
You can put this solution on YOUR website! a.
Volume of the rectangular pyramid:
(length*width*height)/3
(12*8*8)/3 = 768/3 = 256 (check the calculations, I did them in my head)
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b.
Volume of the new pyramid
Was 256 and Jessica bought 40:
256-40 = 216 is the new volume.
Now let's find the new height:
Volume = l*w*h/3
216 = 12*8*h/3 Multiply both sides times 3:
648 = 96h divide both sides by 96
648/96 = h Use your calculator to divide and get your answer
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NOTE:
The volume of a rectangular box is length*width*height. When you take the top of the rectangular box off and bring the four sides together to form the pointy top of the pyramid you discover that the pyramid takes up 1/3 of the volume of the rectangular box. So, the formula for the volume of the pyramid is the same as the volume for the rectangular box divided by 3. I made you a drawing, see below:
