Question

Question 3 please :) (exact values)

Answer 1

Answer:

(a) h = 160 - 5·x

(b) V = 4·x² × h = 4·x² × (160 - 5·x) = 640·x² - 20·x³ = 20·x²·(32 - x)

∴ V = 20·x²·(32 - x)

Step-by-step explanation:

(a) The given dimensions of the cuboid (rectangular prism) are;

'4·x' meters by 'x' meters by 'h' meters

Let the 4·x meters represent the length, 'l', of the cuboid, let the x meters represent the width, 'w', of the cuboid, and let the h meters represent the height 'h' of the cuboid

Therefore, we are given that the cuboid is a wire cage, with the total length of the sides (edges) of the cuboid equal to 640 meters

Therefore, the sum of the edges are;

Top(4·x + x + 4·x + x) + Side(h + h + h + h) + Bottom(4·x + x + 4·x + x) = 640

20·x + 4·h = 640

∴ h = (640 - 20·x)/4 = 160 - 5·x

h = 160 - 5·x

(b) The volume of a cuboid, V, is given as follows;

V = The area of the base of the cuboid × The height of the cuboid

The area of the base of the cuboid = l × w = 4·x × x = 4·x²

The height of the cuboid = h = 160 - 5·x

∴ V = 4·x² × (160 - 5·x) = 640·x² - 20·x³

V = 640·x² - 20·x³ = 20·x²·(32 - x)

∴ V = 20·x²·(32 - x) QED.