Question

I need help please I don’t have a lot of time

Answer 1

Base Shape: Circle

Base Area (exact) = 42.25π mm²

Height of Cylinder = 19 mm

Volume (exact) = 802.75π mm³

Volume (tenth) = 2521.9 mm³

Explanation:

Base Shape

The base shape of a cylinder is a circle.

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Base Area

The formula for the area of a circle is A = πr², where r is the radius.

The diameter of a circle is twice its radius. Therefore, given the diameter of the base of the cylinder is 13 mm, its radius is r = 6.5 mm. So, the exact area of the base can be calculated as follows:

`A=\pi \cdot 6.5^2`

`A = 42.25 \pi\; \sf mm^2`

Therefore, the exact area of the base is 42.25π mm².

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Height of Cylinder

The height of the cylinder is 19 mm.

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Volume

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the circular base, and h is the height of the cylinder. Given the radius is 6.5 mm and the height is 19 mm, the exact volume of the cylinder is:

`V=\pi r^2 h`

`V = \pi \cdot 6.5^2 \cdot 19`

`V = \pi \cdot 42.25 \cdot 19`

`V=802.75 \pi \; \sf mm^3`

So, the exact volume of the cylinder is 802.75π mm³.

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Volume (tenth)

The volume of the cylinder is:

`V=2521.9135026692...\; \sf mm^3`

So, the volume of the cylinder rounded to the nearest tenth is 2521.9 mm³.