Question

unit 2
topic 7
practice
for use after grade 7 advanced, lesson 1.3
if possible, find the value of x so that the value of the surface area is equ
to the value of the volume.
1.
2.

Explanation:

Problem 1:

Step 1: Recall formulas for surface area and volume of a rectangular prism.

The surface area \( S \) of a rectangular prism with length \( l \), width \( w \), height \( h \) is \( S = 2(lw + lh + wh) \). The volume \( V \) is \( V = lwh \). Here, \( l = 10 \) in, \( w = 3 \) in, \( h = x \) in.

So, \( S = 2(10\times3 + 10\times x + 3\times x)=2(30 + 10x + 3x)=2(30 + 13x)=60 + 26x \)

\( V = 10\times3\times x = 30x \)

Step 2: Set surface area equal to volume and solve for \( x \).

Set \( 60 + 26x = 30x \)

Subtract \( 26x \) from both sides: \( 60 = 30x - 26x \)

Simplify: \( 60 = 4x \)

Divide both sides by 4: \( x=\frac{60}{4}=15 \)

Step 1: Recall formulas for surface area and volume of a rectangular prism.

The surface area \( S \) of a rectangular prism with length \( l \), width \( w \), height \( h \) is \( S = 2(lw + lh + wh) \). The volume \( V \) is \( V = lwh \). Here, \( l = 8 \) m, \( w = 4 \) m, \( h = x \) m.

So, \( S = 2(8\times4 + 8\times x + 4\times x)=2(32 + 8x + 4x)=2(32 + 12x)=64 + 24x \)

\( V = 8\times4\times x = 32x \)

Step 2: Set surface area equal to volume and solve for \( x \).

Set \( 64 + 24x = 32x \)

Subtract \( 24x \) from both sides: \( 64 = 32x - 24x \)

Simplify: \( 64 = 8x \)

Divide both sides by 8: \( x=\frac{64}{8}=8 \)

Answer:

\( x = 15 \) inches

Problem 2: