Question

The options are A. 80 mmB.85 mmC.60 mmD.95 mm i think D im not sure

Answer 1

Given:

• Dimensions of cylinder on the left:

Height = 60 mm

Diameter = 32 mm

• Diameter of cylinder on the right:

Height = 100 mm

Diameter = 24 mm

Given that the cylinder on the left is filled to a height of 45 mm, and the same amount was poured in both cylinders, let's find the approximate height filled in the cylinder on the right.

Let's first find the volume of content in the cylinder by the left using the formula:

`V=\pi((d)/(2))^2h`

Where:

d is the diamter = 32 mm

h is the height filled = 45 mm

V is the volume

Thus, we have:

`\begin{gathered} V_{\text{left}}=\pi((32)/(2))^2*45 \\ \\ V_{\text{left}}=\pi(16)^2*45 \\ \\ V_{\text{left}}=256\pi*45=11520\pi mm^3 \end{gathered}`

The volume of the left cylinder is 11520π cubic millimeters.

Now, since the the amount was poured in both cylinders, they will have the same volume.

Substitute 11520π for V and input 24 for d and solve for h to find the height filled in the second cylinder.

We have:

`\begin{gathered} V=\pi((d)/(2))^2h \\ \\ 11520\pi=\pi((24)/(2))^2h \\ \\ 11520\pi=\pi(12)^2h \\ \\ 11520\pi=\pi(144)h \\ \\ 11520\pi=144\pi h \end{gathered}`

Divide both sides by 144π:

`\begin{gathered} (11520\pi)/(144\pi)=(144\pi h)/(144\pi) \\ \\ 80=h \\ \\ h=80mm \end{gathered}`

Therefore, the aproximate height filled in the cylinder on the right is 80 mm.

ANSWER:

80 mm