Question

Need some help. Urgently. Please explain and answer.

Answer 1

Find volume

• πr²h
• π(4)²(10)
• 16π(10)
• 160π

Density=12g/cm³

We know

mAss=Density ×Volume

• 12(160)π
• 1920π
• 6031g

Answer 2

6032 g

Explanation:

The battery can be modeled as a cylinder.

Volume of a cylinder

`\sf V=\pi r^2 h`

where:

• r is the radius
• h is the height

Given:

• r = 4 cm
• h = 10 cm

Substitute the given values into the formula and solve for v:

`\begin{aligned}\textsf{Volume of a cylinder} & =\sf \pi r^2 h \\ \implies \textsf{Volume of the battery} & = \sf \pi (4)^2(10)\\ v& = \sf 160 \pi\:\:cm^3\end{aligned}`

Density equation

`\rho =(m)/(v)`

where:

• 
  `\rho` is density
• m is mass
• v is volume

Given:

`\rho = 12 \frac{\text{g}}{\sf cm^3}`

`v=160 \pi \sf \:\:cm^3`

Substitute the given values into the Density equation and solve for m:

`\begin{aligned}\rho & =(m)/(v)\\\implies 12 \frac{\text{g}}{\sf cm^3} & = (m)/(160 \pi \sf \:\:cm^3)\\m & = 12 \frac{\text{g}}{\sf cm^3} \cdot 160 \pi \sf \:\:cm^3\\m & = 12 \cdot 160 \pi \:\text{g}\\ m & = 1920\pi\:\text{g}\\ m & = 6031.857895...\:\text{g}\end{aligned}`

Therefore, the total mass of the battery to the nearest gram is 6032 g.