Question

1. find the volume and the surface area of the rectangular prism, below.

volume = ____________
surface area = ____________

1. conversion key: 1 carat = 0.2 grams; 1 gram =.035 ounces

an official chicago cubs 2016 world series championship ring weighs 23.2 carats. complete the conversion chart below to find how many ounces the ring weighs.
\frac{23.2 car}{1}cdot\frac{g}{car}cdot\frac{oz}{g}= ____________ ounces (nearest hundredth)

1. if a 1:192 movie set scale model of the empire state building in new york city is 84 inches tall, what is the actual height of the building, in feet?

for the final two points, which of the 5 pizza places from the bar chart is your favorite? choose only one place. if you match my favorite, i will give you 3 points, instead of 2.

Explanation:

Step1: Calculate volume of rectangular prism

The formula for the volume \(V\) of a rectangular prism is \(V = l\times w\times h\), where \(l = 12\) cm, \(w = 4\) cm and \(h = 8\) cm. So \(V=12\times4\times8 = 384\) \(cm^{3}\).

Step2: Calculate surface - area of rectangular prism

The formula for the surface - area \(SA\) of a rectangular prism is \(SA = 2(lw+lh + wh)\). Substitute \(l = 12\) cm, \(w = 4\) cm and \(h = 8\) cm. \(SA=2(12\times4 + 12\times8+4\times8)=2(48 + 96 + 32)=2\times176 = 352\) \(cm^{2}\).

Step3: Convert carats to ounces

Given \(1\) carat \( = 0.2\) grams and \(1\) gram \(=0.035\) ounces. For \(23.2\) carats, first convert to grams: \(23.2\times0.2=4.64\) grams. Then convert grams to ounces: \(4.64\times0.035 = 0.1624\approx0.16\) ounces.

Step4: Calculate actual height of building

The scale is \(1:192\), and the model height is \(84\) inches. Let the actual height be \(h\) inches. Then \(\frac{1}{192}=\frac{84}{h}\), so \(h = 84\times192=16128\) inches. Since \(1\) foot \( = 12\) inches, the actual height in feet is \(\frac{16128}{12}=1344\) feet.

Answer:

Volume = \(384\) \(cm^{3}\)
Surface Area = \(352\) \(cm^{2}\)
\(\frac{23.2\ car}{1}\cdot\frac{0.2\ g}{1\ car}\cdot\frac{0.035\ oz}{1\ g}\approx0.16\) ounces
The actual height of the building is \(1344\) feet.