Question

a toy piece made from plastic is in the shape of a solid hemisphere with a radius of 1.5 centimeters. there are two types of plastic that can be used to make the hemisphere. plastic a contains 1.3 grams per cubic centimeter and costs $0.09 per gram. plastic b contains 1.0 gram per cubic centimeter and costs $0.12 per gram. part a which plastic would result in the lower cost to make the piece? use 3.14 as an approximation for π. a. plastic a b. plastic b part b what is the cost, to the nearest cent, to make one piece using the cheaper plastic? enter the answer in the box. $

Explanation:

Step1: Calculate the volume of the hemisphere

The volume formula for a hemisphere is $V=\frac{2}{3}\pi r^{3}$. Given $r = 1.5$ cm and $\pi=3.14$, we have $V=\frac{2}{3}\times3.14\times(1.5)^{3}=\frac{2}{3}\times3.14\times3.375 = 7.065$ $cm^{3}$.

Step2: Calculate the cost for Plastic A

The mass of Plastic A used is $m_A=1.3\times V=1.3\times7.065 = 9.1845$ grams. The cost $C_A=0.09\times m_A=0.09\times9.1845 = 0.826605\approx0.83$ dollars.

Step3: Calculate the cost for Plastic B

The mass of Plastic B used is $m_B = 1.0\times V=1.0\times7.065=7.065$ grams. The cost $C_B=0.12\times m_B=0.12\times7.065 = 0.8478\approx0.85$ dollars.

Step4: Compare the costs

Since $0.83<0.85$, Plastic A is cheaper.

Answer:

A. Plastic A
$0.83$