Question

The total surface area of a hemispherical ball is 942cm².It is melted and made into small solid identical spherical balls of diameter 2cm each.How many balls can be made?

Answer 1

500 balls can be made using it

Hope this hepls

Answer 2

Answer:

500

Step-by-step explanation:

Solution:

1. Given the surface area, find the radius

2. With the radius, find the volume of the hemisphere

3. Find the volume of the smaller spherical balls

4. Divide to find the number of balls that can be made

Formula Needed:

1. *Total Surface Area of a hemisphere = 3πr²

2. Volume of a hemisphere = 2/3 πr³

2. Volume of a sphere = 4/3 πr³

Taking π as 3.14

STEP 1: Find the radius of the hemisphere

Surface Area of a hemisphere = 3πr²

3πr² = 942

r² = 942 ÷ 3π

r² = 100

r = √100

r = 10 cm

STEP 2: Find the volume of the hemisphere

Volume = 2/3 πr³

Volume = 2/3 π(10)³

Volume = 6280/3 cm³

STEP 3: Find the volume of the small spherical balls

Radius = Diameter ÷ 2

Radius = 2 ÷ 2 = 1 cm

Volume = 4/3 πr³

Volume = 4/3 π(1)³

Volume = 314/75 cm³

STEP 4: Find the number of balls

Number of balls =  6280/3 ÷  314/75

Number of balls = 500

Answer: 500 balls

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Note *:

Total Surface Area of a hemisphere = Surface area of a hemisphere + base area of the hemisphere

Total Surface Area of a hemisphere = 2πr² + πr² = 3πr²