Question

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

Answer 1

Answer:

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