A rectangular block of lead with dimension 43 cm x 53 cm x 63 cm is melted to mould spherical balls of 3 cm radius. How many balls are made? (Round your answer to the nearest whole number and take Pi as 3.14)
volume of lead: 43x53x63 = 6837
volume of ball: 4/3 pi * 3^3 = 113.10
number of balls = 6837/113.10 = 60.45
So, only 60 complete balls can be made.
To find the number of spherical balls that can be made from the rectangular block of lead, we need to calculate the volume of the block and divide it by the volume of each ball.
1. Calculate the volume of the rectangular block:
V_block = length x width x height
V_block = 43 cm x 53 cm x 63 cm
2. Calculate the volume of each spherical ball:
V_ball = (4/3) x Ο x (radius)^3
V_ball = (4/3) x 3.14 x (3 cm)^3
3. Divide the volume of the block by the volume of each ball to get the number of balls:
Number of balls = V_block / V_ball
Let's calculate it step by step:
1. Calculate the volume of the rectangular block:
V_block = 43 cm x 53 cm x 63 cm
= 1,078,929 cm^3
2. Calculate the volume of each spherical ball:
V_ball = (4/3) x 3.14 x (3 cm)^3
= (4/3) x 3.14 x 27 cm^3
= 113.04 cm^3 (rounded to two decimal places)
3. Divide the volume of the block by the volume of each ball to get the number of balls:
Number of balls = V_block / V_ball
= 1,078,929 cm^3 / 113.04 cm^3
β 9547 balls
Therefore, approximately 9547 spherical balls can be made from the rectangular block of lead.