Find the number of lead balls, each with a diameter of 3 cm, that can be made from a sphere of diameter 21 cm.
1. 196
2. 216
3. 256
4. 343
1. 196
2. 216
3. 256
4. 343
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
Correct Answer – Option 4 : 343
Given:
Diameter of sphere = 21 cm
Diameter of lead balls = 3 cm
Formula used:
Volume of sphere = 4/3(πr3)
Calculation:
Let ‘n’ be the number of lead balls that can be made from a sphere
Radius of sphere = 21/2 cm
Radius of lead balls = 3/2 cm
⇒ Volume of sphere = 4/3(πr3)
⇒ Volume of sphere = 4/3[π(21/2)3]
⇒ Volume of lead ball = 4/3[π(3/2)3]
According to the question,
Volume of sphere = n × Volume of lead balls
⇒ 4/3[π(21/2)3] = n × 4/3[π(3/2)3]
⇒ (21/2)3 = n × (3/2)3
⇒ 9261/8 = n × 27/8
⇒ n = 9261/27
⇒ n = 343
∴ The number of lead balls, each with a diameter of 3 cm, that can be made from a sphere of diameter 21 cm is 343.