Question

1. determine the surface area and volume of the rectangular prism. express your answer for surface in square millimeters and for volume in cubic millimeters.
2. how much glass is needed to create a fish tank that has no top, has a length of 15 in, a width of 10 in and a height of 12 in? provide a diagram
3. krispy kritters cereal used to come in a box with a volume of 2 850 cm³. however, the krispy kritters co. designed a new larger box 22.5 cm wide, 6.2 cm deep and 30 cm high. how many more cubic centimetres will the new box hold compared to the old box? provide a diagram.

Explanation:

Problem 3:

Step1: Convert units to millimeters

Length \( l = 4.8\space cm = 48\space mm \), Width \( w = 1.7\space cm = 17\space mm \), Height \( h = 5.9\space cm = 59\space mm \)

Step2: Calculate Surface Area (SA)

Formula: \( SA = 2(lw + lh + wh) \)
\( lw = 48\times17 = 816 \), \( lh = 48\times59 = 2832 \), \( wh = 17\times59 = 1003 \)
\( SA = 2(816 + 2832 + 1003) = 2(4651) = 9302\space mm^2 \)

Step3: Calculate Volume (V)

Formula: \( V = lwh \)
\( V = 48\times17\times59 = 48\times1003 = 48144\space mm^3 \)

Step1: Identify the formula for surface area of open - top rectangular prism

The formula for the surface area (\( SA \)) of a rectangular prism with no top is \( SA=lw + 2lh+2wh \), where \( l = 15\space in \), \( w = 10\space in \), \( h = 12\space in \)

Step2: Substitute the values into the formula

\( lw=15\times10 = 150 \), \( 2lh = 2\times15\times12=360 \), \( 2wh=2\times10\times12 = 240 \)
\( SA=150 + 360+240=750\space in^2 \)

(Diagram: A rectangular prism with length 15 in, width 10 in, height 12 in, and the top face (length×width) missing)

Step1: Calculate the volume of the new box

Formula for volume of a rectangular prism \( V=lwh \) (here, width \( w = 22.5\space cm \), depth \( l = 6.2\space cm \), height \( h = 30\space cm \))
\( V=22.5\times6.2\times30 \)
First, \( 22.5\times6.2 = 139.5 \), then \( 139.5\times30=4185\space cm^3 \)

Step2: Calculate the difference in volume

Difference \( = 4185 - 2850=1335\space cm^3 \)

Answer:

Surface Area: \( 9302\space mm^2 \), Volume: \( 48144\space mm^3 \)

Problem 4: