can someone help me?

Question

An observatory has the shape of a right circular cylinder surmounted by a hemisphere.

Consider the surface area of the observatory, if the radius of the cylinder is 12 ft and its altitude measures 30 ft.

1. Find the exact lateral area (in square feet) of the cylinder.

(__________)ft²

1. Find the exact surface area (in square feet) of the curved part of the hemisphere.

(__________)ft²

1. What is the surface area (in square feet) of the observatory? Use the calculator value of 𝜋. (Round your answer to two decimal places.)

__________ft²

1. If 1 gallon of paint covers 300 ft² and you can only purchase full gallons of paint, how many gallons must be purchased to paint the surface if it requires two coats? (Round your answer up to the nearest whole number.)

__________ gal

Answer 1

Altitude is another word for height in a cylinder. This you just need a few formulas to do this. I won’t solve them for you, but I will give you the formulas you need and check your math if you complete them today and comment your answers.

1. The formula for lateral surface area in a cylinder is 2πrh (this makes sense since into the circumference or the cylinder times the height)
2. The formula for the surface area of the curve in a hemisphere is 2πr² (this is half the surface area for a sphere so this also makes sense)
3. If you calculate the first two correctly and the outside of the observatory is made of these two parts, it should be easy to see what you need to do for this question. (Ask me in the comments if this isn’t clear)
4. After you correctly answer #3, this is where you get to apply your knowledge to a “real world” situation. If you need enough paint to cover the surface of the observatory twice and it only comes in full 300ft² gallons, how many cans do you need? (Ask me in the comments if the process isn’t clear)