Question

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.

Answer 1

Answer:

The radius of a base of a cone is 3.74 cm

Step-by-step explanation:

SOLUTION:

Given :  

Radius of hemisphere, r = 7 cm

Height of a right circular cone ,h = 49 cm

Let, R be radius of a base of a cone

The hemisphere is cast into the right circular cone, Therefore

Volume of hemisphere =  Volume of cone

⅔ πr³ = ⅓ πR²h  

2 r³ = R²h  

2 × 7³ = R² × 49

2 × 49 × 7 = 49R²

R² = (2 × 49 × 7)/49

R² = 14

R = √14  

R = 3.74 cm

Hence, the radius of a base of a cone is 3.74 cm

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

ANSWER:--------------

{ hemisphere = volume of cone}

{2/3 x π x 7³ = 1/3 x π x r² x 49  (divide both sides by π)}

{2/3 x 7³ = 1/3 x r² x 49}

{228 2/3 = 16 1/3 r²}

{r² = (228 2/3) / (16 1/3)}

{   = 14}

{r = √14}

{r = 3.74cm }

hope it helps:--

T!—!ANKS!!!!