Question

right prism r and oblique prism s are shown, with dimensions in units. prism r diagram 7, 4, 12. prism s diagram 7, 4, 12 (perpendicular height), 15 (slant). complete the statements to compare the volumes of the prisms. the volume of prism s is dropdown cubic units. the volume of prism s is dropdown the volume of prism r.

Explanation:

Step1: Recall the volume formula for a prism

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

Step2: Calculate the base area for both prisms

For both prisms R and S, the base is a rectangle with length \( l = 7 \) and width \( w = 4 \). So the area of the base \( B \) is \( B = l \times w = 7 \times 4 = 28 \) square units.

Step3: Determine the height for prism S

For prism S (an oblique prism), the height is the perpendicular distance between the bases, which is given as \( 12 \) units (the dashed vertical segment with the right angle).

Step4: Calculate the volume of prism S

Using the volume formula \( V = B \times h \), substitute \( B = 28 \) and \( h = 12 \). So \( V_S = 28 \times 12 = 336 \) cubic units.

Step5: Calculate the volume of prism R (for comparison)

For prism R (a right prism), the height is the vertical edge, which is \( 12 \) units. Using the same base area \( B = 28 \), the volume \( V_R = 28 \times 12 = 336 \) cubic units. So the volume of prism S is equal to the volume of prism R.

Answer:

The volume of prism S is \( 336 \) cubic units.
The volume of prism S is equal to the volume of prism R.