Question

What is the Formula to find the Total surface area of a semi-cylinder?

Answer 1

The top and bottom of the cylinder added together make one circle, so the formula for that is πr^2. The rectangle where the cylinder is cut in half can be worked out with 2hr. The curved side can be worked out with πhr. Add the formulae together to get 2hr+πhr+πr^2. Simplify that as you like (the first two terms can be simplified to hr(π+2)).

Answer 2

`\textsf{Total surface area of semi cylinder = } \boxed{\sf \pi r(r+h)}`

Explanation:

The total surface area of a cylinder is the sum of the areas of the two bases and the lateral surface. The lateral surface is the curved surface that runs around the cylinder.

The formula for the total surface area of a cylinder is:

`\boxed{\sf TSA =2 \pi rh+ 2\pi r^2 + =2\pi r(h + r)}`

where:

• TSA is the total surface area of the cylinder.
• π is the mathematical constant pi (approximately equal to 3.14)
• r is the radius of the cylinder
• h is the height of the cylinder

Since we know that,

Total surface area of semi cylinder is equal to half of the total surface area of full cylinder.

So,

`\textsf{Total surface area of semi cylinder = } \sf (1)/(2)* 2\pi r(r+h)`

`\textsf{Total surface area of semi cylinder = } \sf \pi r(r+h)`

Therefore,

`\textsf{Total surface area of semi cylinder = } \boxed{\sf \pi r(r+h)}`