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Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 ft and a height of 3.5 ft. How much fabric does Allison need? Round to the nearest square foot.

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JeanaShupp

Answer: 33 square feet

Step-by-step explanation:

Given: The diameter of cylindrical garbage can = 3 ft

Then Radius =\(\frac{3}{2}\) ft.

The height of cylindrical garbage can = 3.5 ft.

We know that the lateral surface area is given by :-

\(L.A.=2\pi r h\)

Then the lateral surface area of the cylindrical garbage can will be :-

\(L.A.=2\pi(\frac{3}{2})(3.5)\\\\\Rightarrow\ L.A.=(3.14)(10.5)\\\\\Rightarrow\ L.A.=32.97\approx33\ ft.^2\)

Hence, Alison needs 33 square feet of fabric.

The cylindrical can have a diameter of 3 ft and a height of 3.5 ft. The lateral surface area of the cylindrical garbage can is 33ft cube.

What is the lateral surface area of a cylinder?

The lateral surface area of a cylinder is the product of the height h, pie, and twice the radius r.

The lateral surface area of a cylinder = 2πrh

The diameter of a cylindrical garbage can = 3 ft

The radius of the cylindrical garbage can = 3/2ft.

The height of the cylindrical garbage can = 3.5 ft.

The lateral surface area of a cylinder = 2πrh

\(2 \times 3.14 \times (3/2) \times 3.5\\= 3.14 \times 3.5\\\rm = 32.97 ft^2\)

Thus, the lateral surface area of the cylindrical garbage can is 33ft.

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