Question

1. a rectangular prism has a width of x centimetres. its length is 4 cm more than its width and its height is 5 cm more than its width. find the a)the area b) volume. a = lw = 4×5 = 20

Explanation:

Step1: Determine the length and height

Given width \( w=x\) cm, length \( l=(x + 4)\) cm, height \( h=(x + 5)\) cm.

Step2: Calculate the surface area formula

The surface area \(A\) of a rectangular prism is \(A = 2(lw+lh+wh)\).
Substitute \(l=x + 4\), \(w=x\), \(h=x + 5\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Calculate the volume formula

The volume \(V\) of a rectangular prism is \(V=l\times w\times h\).
Substitute \(l=x + 4\), \(w=x\), \(h=x + 5\) into the formula:

$$
LATEXBLOCK1
$$

Answer:

a) The surface area \(A = 6x^{2}+36x + 40\) square - centimeters.
b) The volume \(V=x^{3}+9x^{2}+20x\) cubic - centimeters.