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The curved surface area of a cylinder whose height is 14 feet and radius is 6 feet is 527.79ft2

Q: What is the surface area of a cylinder whose height is 14 feet and radius is 6 feet?

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754 square feet.

The formular for the surface area of a cylinder is 2(pi)rh + 2(pi)r2 where r=radius and h=height and pi=3.14 SA= 2 x 3.14 x 15 x 30 + 2 x 3.14 x 152 =4239

Volume of a cylinder = πr²hV= 3.14159 × (3)² × 7V= 197.92 ft³

Imagine taking the ends off the cylinder, cutting the side down from end to end and unrolling the side; this creates a rectangle with the height of the cylinder along one edge and the circumference of the end along the other. Thus area of side = circumference × height. The ends of the cylinder are circles, thus: area = π × radius² → radius = √(area ÷ π) circumference = 2 × π × radius → circumference = 2 × π × √(area ÷ π) = 2 × √(area × π) → area side = 2 × √(area × π) × height → surface area of cylinder = 2 × area ends + area side → surface area = 2 × 11 units² + 2 × √(11 units² × π) × 11 units → surface area = 22 + 22 × √(11π) units² → surface area ≈ 22 + 129.33 units² ≈ 151 units²

I'm quite sure this is impossible to prove, because the volume of a sphere is not equal to the volume of a cylinder with the same radius and height equal to the sphere's diameter. This can be shown as: Volume of sphere = (4*pi*r3) / 3. Volume of cylinder = pi*r2*h. Here, the height, h, of the cylinder = d = 2r. So, the volume of the cylinder = pi*r2*2r = 2*pi*r3, which obviously does not equal the volume of the sphere. The volume of half a sphere (with radius r) is equal to the volume of a cylinder(whose height is equal to its radius, r) minus the volume of a cone with the same height and radius. Therefore, the volume of a sphere is just double that. If you follow the nearby link, you can see a nice demonstration of that.

Related questions

The surface are of a cylinder whose radius is 10cm and height is 20cm is 1884.96cm2

A cylinder whose radius is 6 and height is 14 has a surface area of 754 units2

A cylinder whose radius is 5 and height is 7 has a surface area of 377 units2

This cylinder's height is 6 (5.98) units.

847.8

37.68

A cylinder whose radius is 2cm and height is 8cm has a total surface area of approximately 125.66cm2 {ADDED} To explain that further, the formula is pi*r^2 X h where r is the radius and h the height.

The surface area of a cylinder is 2*pi*radius*height. In this case it would be 2*pi*5*10 = 314.16

Surface area = 673.87 units2

345.6 units2

1,979.2 units2

251.3 units2