Question

I included a photo with the information! Here are the questions. A thorough explanation and diagram would help IMMENSELY. Thank you so much!

Question 1: reate 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.


Question 2: Create a labeled diagram of the Egyptian. 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.

Question 3: 1. To impress management, you decide to propose your own original candle design based on solid figures. Make your candle design attractive and make sure it will be practical to manufacture. Draw the candle in the space below and label the drawing with dimensions. Then write an equation for the volume of the candle in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in standard form.

Answer 1

1) Labeled diagram in the first figure attached

Volume of the rectangular prism: x^2*(x-1) = x^3 - x^2 ; x in cm, volume in cm^3

2) Labeled diagram in the second figure attached

Volume of the right square pyramid: (1/3)*(x^2)*21 = 7*x^2, x in cm, volume in cm^3

3) A cylinder is proposed, where x is the radius of the base and the height is 4 times the radius. Labeled diagram in the third figure attached .

Volume of the cylinder: π*x^2*(4*x) = 4*π*x^3, x in cm, volume in cm^3

Answer 2

1. If the length of the side of the base of the Brick is x then, the volume in cubic centimeters of the candle is:
V = x² (x - 1)
or
V = x³ - x²

2. If the length of the side of the base of the Pyramid is x then, the volume in cubic centimeters of the candle is:
V = (1/3) (21) x²
or
V = 7x²

3. The new design involves the two original designs, with the Pyramid placed on top of the Brick. Therefore, the volume is:
V = x³ - x² + 7x²
or
V = x³ + 6x²