SOLUTION: You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest candle designs, the Brick and the Egyptian. The original Brick was a cube 8 cen
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-> SOLUTION: You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest candle designs, the Brick and the Egyptian. The original Brick was a cube 8 cen
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Question 934741: You work for the BeeSwaks Candle Company and have been asked to update two of the company’s earliest candle designs, the Brick and the Egyptian. The original Brick was a cube 8 centimeters on a side. The original Egyptian was a pyramid 21 centimeters tall with a square base 10 centimeters on a side.
Improvements in the manufacturing process have made it possible to change the design of these candles for a fresh new look and improved profit. You have been asked to work within the following guidelines:
The Brick:
Shape- rectangular prism
Base- dimensions can vary, but it must be a square
Height- 1 cm less than the side length of the base
The Pyramid:
Shape- right square pyramid
Base- same dimensions as base of the Brick
Height- 21 cm
Question: Create a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Volume of a pyramid= (1/3)Area of the base x Height
You can put this solution on YOUR website! Drawing the picture easier done on paper than through sophisticated software and posting to an image hosting service.
The formulas for the volumes are easily done here.
BRICK VOLUME:
The two bottom dimensions are each x.
Volume is and necessary restriction is .
Standard form is probably but you might really want general form, .
PYRAMID VOLUME:
You already have the basic formula so this should be no trouble.
Volume is
simplifiable to .
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