Question

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V = lwh P = 2(l + w

Answer 1

Answer:

The quadratic y that best models the volume = 70L - 5L^2

Step-by-step explanation:

Since the formula for calculating the perimeter of a rectangle = 2(L+W) and the perimeter of the base of this box in question must be 28cm. We can always find the sum of the length and the width of the rectangular base.

2(L+W) = 28

L+W = 28/2

L + W = 14

The sum of the box's length and width width = 14cm.

Again, we were informed that the box must have a height no of 5cm. So to be able to have an idea of what its volume will be like, we will be needing the formula for calculating the volume of a cuboid which the box is. The formula for the volume is:

Length×width×height

Since the sum of the length and the width of the base of the box must be -

L + W = 14

We will then make "W"(width) the subject of the formula

L + W = 14

W = 14 - L

Now, we will substitute W for 14 - L in the formula for calculating the volume of a cuboid

Volume of a cuboid = L × W × H

Since h = 5cm then:

= L × (14 - L) × 5

= (14L - L^2) × 5

= 70L - 5L^2

Therefore, the quadratic equation that best models the volume of the box is = 70L - 5L^2

Answer 2

Answer:

The quadratic equation that best models the volume of the box (in terms of W) is:

$70W-5W^2$

Step-by-step explanation:

The perimeter of the rectangular base = 28cm

Perimeter of a rectangle = 2(L+W)

2(L+W)=28

L+W=14

L=14-W

Volume of the Box= LWH

Since L=14-W and Height Of the Box= 5cm

Volume of the Box= (14-W)W X 5

$=5(14W-W^2)\\ =70W-5W^2$