Question

The total surface area of a solid hemisphere is 75 times the area of a circle whose diameter is 6 cm Whats
the radius (in cm) of the hemisphere?
​

Answer 1

Answer:

Given that the total surface area of the solid hemisphere,

3πr

2

=675πsq.cm

⇒r

2

=225

Now the curved surface area of the solid hemisphere,

CSA=2πr

2

=2π×225=450πsq.cm

Answer 2

Answer :

›»› The radius of the hemisphere is 15 cm.

Given :

• The total surface area of a solid hemisphere is 75 times the area of a circle whose diameter is 6 cm.

To Find :

• The radius of the hemisphere in cm.

Solution :

Let, us assume that the radius of the hemisphere is "r"

→ Diameter of circle = 6 cm

→ Radius of circle = Diameter/2

→ Radius of circle = 6/2

→ Radius of circle = 3 cm

The total surface area of a solid hemisphere is 75 times the area of a circle.

→ Total surface area of hemisphere = 75 * Area of circle.

→ 3πr² = 75 * πr²

Cancel π by both sides,

→ 3r² = 75 * r²

→ 3 * r² = 75 * 3²

→ 3 * r² = 75 * 3 * 3

Cancel 3 by both sides,

→ r² = 75 * 3

→ r² = 225

→ r = √225

→ r = 15

║Hence, the radius of the hemisphere is 15 cm.║