7. higher order thinking the cylinder shown is a steel tube that weighs 0.2835 pound per cubic inch. the…

7. higher order thinking the cylinder shown is a steel tube that weighs 0.2835 pound per cubic inch. the inner part of the tube is hollow. what is the weight of the tube? use 3.14 for π, and round to the nearest tenth.

7. higher order thinking the cylinder shown is a steel tube that weighs 0.2835 pound per cubic inch. the inner part of the tube is hollow. what is the weight of the tube? use 3.14 for π, and round to the nearest tenth.

Answer

Explanation:

Step1: Calculate outer - radius and inner - radius

Outer diameter is 5 in, so outer radius $R=\frac{5}{2}=2.5$ in. Inner diameter is $2\frac{3}{4}=\frac{11}{4}$ in, so inner radius $r = \frac{11}{8}=1.375$ in. Length of cylinder $h = 8\frac{3}{4}=\frac{35}{4}$ in.

Step2: Calculate volume of the tube

Volume of a hollow - cylinder $V=\pi h(R^{2}-r^{2})$. Substitute $\pi = 3.14$, $h=\frac{35}{4}$, $R = 2.5$, and $r = 1.375$ into the formula. $V=3.14\times\frac{35}{4}\times(2.5^{2}-1.375^{2})$ First, calculate $2.5^{2}=6.25$ and $1.375^{2}=1.890625$. Then $2.5^{2}-1.375^{2}=6.25 - 1.890625 = 4.359375$. $V=3.14\times\frac{35}{4}\times4.359375$ $V = 3.14\times38.206640625=120.0698416$ in³.

Step3: Calculate weight of the tube

Weight per cubic - inch is 0.2835 pound. So weight $W=0.2835\times V$. $W=0.2835\times120.0698416\approx34.0$ pounds.

Answer:

34.0 pounds