The diagram shows a solid formed by joining a hemisphere, of radius rcm, to a cylinder, of radius rcm and height hcm. The total height of the solid is 18 cm and the surface area is 205pie cm? Find the value of r and the value of h cm

Step-by-step explanation:

The total surface area of the sphere = 2πr²

Total surface area of the cylinder = 2πr²+2πrh

Total surface area of the solid = 4πr²+2πrh

r is the radius of the sphere and the cylinder

h is the height of the cylinder

Total surface area of the solid = 2πr(r+h)

If the total height of the solid is 18 cm, then r+h = 18cm

Given the Total surface area of the solid = 205π cm

205π = 2πr(r+h)

205π = 2πr(18)

205π = 36πr

205 = 36r

Divide both sides by 36

205/36 = 36r/36

r = 5.69cm

Since  r+h = 18cm

5.69+h = 18

h = 18-5.69

h = 12.31cm

40 minutes

step-by-step explanation:

add the time and multiply by 2

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240