Sure, here is the step by step solution:

Step 1: We know that the volume of a sphere is given by the formula (4/3)πr³.

Step 2: Let's say the radius of the original ball is R. So, the volume of the original ball is (4/3)πR³.

Step 3: The radius of the smaller balls is half of the original, so it's R/2. The volume of each smaller ball is (4/3)π(R/2)³.

Step 4: The number of smaller balls that can be made from the original ball is the volume of the original ball divided by the volume of a smaller ball.

Step 5: So, the number of smaller balls = [(4/3)πR³] / [(4/3)π(R/2)³].

Step 6: Simplifying this, we get the number of smaller balls = R³ / (R/2)³ = (2³) = 8.

So, 8 smaller balls can be made from the original ball.

Question

Sure, here is the step by step solution:

Step 1: We know that the volume of a sphere is given by the formula (4/3)πr³.

Step 2: Let's say the radius of the original ball is R. So, the volume of the original ball is (4/3)πR³.

Step 3: The radius of the smaller balls is half of the original, so it's R/2. The volume of each smaller ball is (4/3)π(R/2)³.

Step 4: The number of smaller balls that can be made from the original ball is the volume of the original ball divided by the volume of a smaller ball.

Step 5: So, the number of smaller balls = [(4/3)πR³] / [(4/3)π(R/2)³].

Step 6: Simplifying this, we get the number of smaller balls = R³ / (R/2)³ = (2³) = 8.

So, 8 smaller balls can be made from the original ball.

Knowee AI · Accepted Answer

Sure, here is the step by step solution:

Step 1: We know that the volume of a sphere is given by the formula (4/3)πr³.

Step 2: Let's say the radius of the original ball is R. So, the volume of the original ball is (4/3)πR³.

Step 3: The radius of the smaller balls is half of the original, so it's R/2. The volume of each smaller ball is (4/3)π(R/2)³.

Step 4: The number of smaller balls that can be made from the original ball is the volume of the original ball divided by the volume of a smaller ball.

Step 5: So, the number of smaller balls = [(4/3)πR³] / [(4/3)π(R/2)³].

Step 6: Simplifying this, we get the number of smaller balls = R³ / (R/2)³ = (2³) = 8.

So, 8 smaller balls can be made from the original ball.

A spherical ball of lead is melted and made into identical smaller balls of radius equal to half of the radius of the original one. How many such balls can be made?

Question

Solution

Similar Questions

Upgrade your grade with Knowee