Answer:
Question 1: C. 4 × 3 × 2 × [tex]\frac{1}{8}[/tex] × [tex]\frac{1}{8}[/tex] × [tex]\frac{1}{8}[/tex]
Question 2: The volume is [tex]\frac{1}{12}[/tex] or 0.083333333
Question 3: The volume fo the solid figure is 234
Step-by-step explanation:
1. Volume of a rectangular prism = (length × width × height) cubic units
Length = 4 × [tex]\frac{1}{8}[/tex]
Width = 3 × [tex]\frac{1}{8}[/tex]
Height = 2 × [tex]\frac{1}{8}[/tex]
Volume = 4 × [tex]\frac{1}{8}[/tex] × 3 × [tex]\frac{1}{8}[/tex] × 2 × [tex]\frac{1}{8}[/tex]
Volume = 4 × 3 × 2 × [tex]\frac{1}{8}[/tex] × [tex]\frac{1}{8}[/tex] × [tex]\frac{1}{8}[/tex]
So the correct option is:
C. 4 × 3 × 2 × [tex]\frac{1}{8}[/tex] × [tex]\frac{1}{8}[/tex] × [tex]\frac{1}{8}[/tex]
2.
We have to fold the shape into a rectangular prism, look at the picture
Volume of a right rectangular prism = (length × width × height)
Length = [tex]\frac{1}{3}[/tex]
Width = [tex]\frac{1}{3}[/tex]
Height = [tex]\frac{3}{4}[/tex]
Volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{4}[/tex]
Multiply [tex]\frac{1}{3}[/tex] times [tex]\frac{1}{3}[/tex] by multiplying numerator times numerator and denominator times denominator.
[tex]\dfrac{ 1 \times 1 }{ 3 \times 3 } \times \left( \dfrac{ 3 }{ 4 } \right)[/tex]
Do the multiplications in the fraction [tex]\dfrac{ 1 \times 1 }{ 3 \times 3 }[/tex]
[tex]\dfrac{ 1 }{ 9 } \times \left( \dfrac{ 3 }{ 4 } \right)[/tex]
Multiply [tex]\frac{1}{9}[/tex] times [tex]\frac{3}{4}[/tex] by multiplying numerator times numerator and denominator times denominator.
[tex]\dfrac{ 1 \times 3 }{ 9 \times 4 }[/tex]
Do the multiplications in the fraction [tex]\dfrac{ 1 \times 3 }{ 9 \times 4 }[/tex]
[tex]\frac{3}{36}[/tex]
Reduce the fraction [tex]\frac{3}{36}[/tex] to the lowest terms by extracting and canceling out 3
Fraction form: [tex]\frac{1}{12}[/tex]
or
Decimal form: 0.083333333
So the volume of the right rectangular prism is [tex]\frac{1}{12}[/tex]
3. Look at the picture with the solid figure labeled
We can think of this shape as two different prisms ( A and B)
Volume of A = 4.5 × 6 × 6.5 = 175.5
Volume of B = 3 × 3 × 6.5 = 58.5
Total volume of the whole figure = 175.5 + 58.5
175.5 + 58.5 = 234
So the volume of the solid figure is 234
