QuestionTentukan tinggi tiang silinder dengan isi padu $404 \mathrm{~cm}^{3}$ dan jejari $2 \mathrm{~cm}$ .

Studdy Solution

STEP 1

Assumptions1. The volume of the medal is $404 \mathrm{~cm}^{3}$ . The volume of the crescent is $60 \mathrm{~cm}^{3}$
3. The radius of the cylinder is $\mathrm{~cm}$
4. The volume of the cylinder is equal to the combined volume of the medal and the crescent

STEP 2

First, we need to find the total volume of the medal and the crescent. We can do this by adding the volume of the medal and the volume of the crescent.
$Total\, volume = Volume\, of\, medal + Volume\, of\, crescent$

STEP 3

Now, plug in the given values for the volume of the medal and the volume of the crescent to calculate the total volume.
$Total\, volume =404 \mathrm{~cm}^{3} +60 \mathrm{~cm}^{3}$

STEP 4

Calculate the total volume.
$Total\, volume =404 \mathrm{~cm}^{3} +60 \mathrm{~cm}^{3} =464 \mathrm{~cm}^{3}$

STEP 5

The volume of a cylinder is given by the formula $V = \pi r^{2}h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height. We can rearrange this formula to solve for the height $h$ .
$h = \frac{V}{\pi r^{2}}$

STEP 6

Now, plug in the values for the volume and the radius to calculate the height.
$h = \frac{464 \mathrm{~cm}^{3}}{\pi \times (2 \mathrm{~cm})^{2}}$

STEP 7

Calculate the height of the cylinder.
$h = \frac{464 \mathrm{~cm}^{3}}{\pi \times4 \mathrm{~cm}^{2}} =37 \mathrm{~cm}$ The height of the cylinder is $37 \mathrm{~cm}$ .

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