Q 41 - Calculus

Question

Find each mass described in Exercises 41–48.

The mass of a block of copper that has a square base with sides measuring 20 centimeters and a height of 13 centimeters. Copper has a density of 8.93 grams per cubic centimeter.

Step-by-Step Solution

Answer

The mass of copper block is 46,436 grams 

Step 1: Given Information

The mass of a block of copper that has a square base with sides measuring 20 centimeters and a height of 13 centimeters with density of 8.93 grams per cubic

centimeter.

Step 2: Formulas

The density of a substance is the mass per unit volume 

The formula for density is 

$$\begin{gathered} \rho =\frac{M}{V} \\ M is the mass and V is the volume \\ V= lbh \\ l is length , b is the width and h is the height of the cuboid \end{gathered}$$

Step 3: Find Volume

copper block has square base . so length and width are same 

$$\begin{gathered} l=20, b=20 , h=13 \\ Volume = \left(20\right)\left(20\right)\left(13\right) \\ Volume = 5,200 \end{gathered}$$

Step 4: Find Mass

$$\begin{gathered} \rho =\frac{M}{V} \\ V=5200 and \rho =8.93 \\ 8.93=\frac{M}{5200} \\ 8.93\left(5200\right)=M \\ M=46,436 \end{gathered}$$

The mass of copper block is 46,436 grams