Question

question 11: standard g.gmd.4
volume has cubic units (in³) and area has ______ units.
a. units (in)
b. quadrupled units (in⁴)
c. no units
d. squared units (in²)
question 12: standard g.gmd.3
if the base of a triangular prism is 12 cm² and the height is 4 cm, what is the volume?
a. 48
b. 16
c. 24
d. 12

Explanation:

Question 11

To determine the units of area, recall that volume (3 - dimensional) has cubic units (e.g., \( \text{in}^3 \)). Area is a 2 - dimensional measurement. For example, the area of a square with side length \( s \) is \( A = s\times s=s^{2} \), so its units are the square of the linear unit (e.g., \( \text{in}^2 \)). Option a is linear units (for length), option b is quartic units (not for area), option c is incorrect as area has units. So the correct option is d.

Step 1: Recall the formula for the volume of a triangular prism

The volume \( V \) of a prism is given by the formula \( V=B\times h \), where \( B \) is the area of the base and \( h \) is the height of the prism.

Step 2: Substitute the given values

We are given that \( B = 12\space\text{cm}^2 \) and \( h = 4\space\text{cm} \). Substituting these values into the formula, we get \( V=12\times4 \).

Step 3: Calculate the product

\( 12\times4 = 48 \).

Answer:

d. Squared units (\( \text{in}^2 \))

Question 12