Rectangular Prism Volume - SSAT Middle Level Quantitative

1. If $l$ doubles while $w$ and $h$ stay the same, how does the volume $V$ change?

   The volume doubles, $V \to 2V$. Since volume is proportional to length, doubling length multiplies volume by 2.

2. What is the volume of a rectangular prism with $l = 3$, $w = \frac{2}{3}$, and $h = 9$?

   $18$. Volume computation includes fractions: $3 \times \frac{2}{3} \times 9 = 18$.

3. What is the volume of a rectangular prism with $l = 1.2$, $w = 5$, and $h = 2$?

   $12$. Decimal multiplication yields volume: $1.2 \times 5 \times 2 = 12$.

4. What is the base area $B$ of a rectangular prism with base length $l$ and base width $w$?

   $B = lw$. The base area of a rectangular prism is the area of its rectangular base, found by multiplying length and width.

5. If $l$, $w$, and $h$ each double, what happens to the volume $V$?

   The volume becomes $8V$. Doubling all dimensions scales volume by $2^3 = 8$, as volume is cubic.

6. What is the formula for volume written as base area $B$ times height $h$ for a rectangular prism?

   $V = Bh$. For prisms, volume is the product of the base area and the height perpendicular to that base.

7. Identify the error: A student wrote $V = 2l + 2w + 2h$ for a rectangular prism's volume. What is correct?

   Correct formula: $V = lwh$. The student's formula is for perimeter of the faces, not volume, which requires multiplication of dimensions.

8. What is the volume of a rectangular prism with $l = 5$, $w = 3$, and $h = 4$?

   $60$. Volume is the product of length, width, and height: $5 \times 3 \times 4 = 60$.

9. If $h$ is cut in half while $l$ and $w$ stay the same, how does the volume $V$ change?

   The volume becomes $\frac{1}{2}V$. Halving height multiplies volume by $\frac{1}{2}$, due to direct proportionality.

10. What is the volume of a rectangular prism with $l = 2.5$, $w = 4$, and $h = 3$?

    $30$. Handle decimal dimensions by multiplication: $2.5 \times 4 \times 3 = 30$.

11. A prism has base area $B = 12$ and height $h = 7$. What is its volume?

    $84$. Volume is base area times height: $12 \times 7 = 84$.

12. What is the volume of a rectangular prism with $l = 10$, $w = 2$, and $h = 1$?

    $20$. Volume equals length times width times height: $10 \times 2 \times 1 = 20$.

13. A prism has dimensions $4\text{ ft}$ by $3\text{ ft}$ by $2\text{ ft}$. What is its volume in $\text{ft}^3$?

    $24\text{ ft}^3$. Multiply dimensions for volume: $4 \times 3 \times 2 = 24$ cubic feet.

14. A rectangular prism has $V = 24\text{ in}^3$, $l = 4\text{ in}$, $w = 2\text{ in}$. What is $h$?

    $3\text{ in}$. Height is volume divided by length times width: $h = \frac{24}{4 \times 2}$, in inches.

15. What is the volume of a rectangular prism with $l = 6$, $w = 6$, and $h = 2$?

    $72$. Calculate by multiplying dimensions: $6 \times 6 \times 2 = 72$.

16. A rectangular prism has volume $V = 150$, length $l = 10$, and height $h = 5$. What is width $w$?

    $3$. Determine width by dividing volume by length times height: $w = \frac{150}{10 \times 5}$.

17. What is the volume of a rectangular prism with dimensions $8\text{ m}$ by $2\text{ m}$ by $3\text{ m}$?

    $48\text{ m}^3$. Multiply the three dimensions: $8 \times 2 \times 3 = 48$, with cubic meter units.

18. What is the volume of a rectangular prism with $l = \frac{1}{2}$, $w = 6$, and $h = 4$?

    $12$. Multiply fractional and whole number dimensions: $\frac{1}{2} \times 6 \times 4 = 12$.

19. A rectangular prism has volume $V = 72$, width $w = 3$, and height $h = 4$. What is length $l$?

    $6$. Find length by dividing volume by width times height: $l = \frac{72}{3 \times 4}$.

20. A rectangular prism has volume $V = 96$, length $l = 8$, and width $w = 4$. What is height $h$?

    $3$. Solve for height by dividing volume by the product of length and width: $h = \frac{96}{8 \times 4}$.

21. What are the correct cubic units for the volume of a rectangular prism measured in centimeters?

    cubic centimeters, $\text{cm}^3$. Volume measures three-dimensional space, so units are the linear unit raised to the third power.

22. What is the volume of a rectangular prism with $l = 9$, $w = 4$, and $h = 5$?

    $180$. The product of the dimensions gives volume: $9 \times 4 \times 5 = 180$.

23. A box measures $30\text{ cm}$ by $20\text{ cm}$ by $10\text{ cm}$. What is its volume in $\text{cm}^3$?

    $6000\text{ cm}^3$. Volume is the product of dimensions: $30 \times 20 \times 10 = 6000$ cubic centimeters.

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