Question

warm-up
write a number or expression for the volume of each box.

Explanation:

Step1: Volume formula for rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\) (length × width × height).

Step2: Calculate volume of Box A

For Box A, \(l = 4\), \(w = 4\), \(h = 20\).
\(V_A=4\times4\times20\)
\(V_A = 16\times20=320\)

Step3: Calculate volume of Box B

For Box B, \(l = 8\), \(w = 2\), \(h = 10\).
\(V_B=2\times8\times10\)
\(V_B=16\times 10 = 160\)

Step4: Calculate volume of Box C

For Box C, \(l=x + 8\), \(w=x + 8\), \(h=x\).
\(V_C=(x + 8)\times(x + 8)\times x\)
Using \((a + b)^2=a^{2}+2ab + b^{2}\), \((x + 8)^2=x^{2}+16x + 64\)
So \(V_C=x(x^{2}+16x + 64)=x^{3}+16x^{2}+64x\)

Answer:

Box	Volume (cubic units)
B	160
C	\(x^{3}+16x^{2}+64x\)