Question

1. 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
2. krispy kritters cereal used to come in a box with a volume of 2850 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 4:

Step1: Identify the formula for surface area (no top)

A fish tank with no top is a rectangular prism with one face (the top) missing. The formula for the surface area (\(SA\)) of a rectangular prism is \(SA = 2lw + 2lh + 2wh\), but since there's no top, we remove the \(lw\) term for the top. So the formula becomes \(SA = lw + 2lh + 2wh\), where \(l = 15\) in (length), \(w = 10\) in (width), and \(h = 12\) in (height).

Step2: Calculate each term

• Calculate \(lw\): \(15 \times 10 = 150\) square inches.
• Calculate \(2lh\): \(2 \times 15 \times 12 = 360\) square inches.
• Calculate \(2wh\): \(2 \times 10 \times 12 = 240\) square inches.

Step3: Sum the terms

Add the three terms together: \(150 + 360 + 240 = 750\) square inches.

Step1: Calculate the volume of the new box

The volume (\(V\)) of a rectangular prism is given by the formula \(V = l \times w \times h\), where \(l = 22.5\) cm (width, we can consider width as length here), \(w = 6.2\) cm (depth, consider as width), and \(h = 30\) cm (height). So \(V = 22.5 \times 6.2 \times 30\).

First, calculate \(22.5 \times 6.2 = 139.5\). Then, multiply by 30: \(139.5 \times 30 = 4185\) cubic centimeters.

Step2: Find the difference in volume

The old box has a volume of \(2850\) \(cm^3\). Subtract the old volume from the new volume: \(4185 - 2850 = 1335\) cubic centimeters.

Answer:

The amount of glass needed is \(\boldsymbol{750}\) square inches. (Diagram: A rectangular prism with length 15 in, width 10 in, height 12 in, with the top face (length × width) not included. Label the length, width, and height on the diagram.)

Problem 5: