Complete Question
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 7 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches.Which of the Following could be used to calculate the volume of water in the vase?
Answer:
[tex]V_w= \pi (3)^2(12) - 8(4/3) \pi(1.5)^3[/tex]
Step-by-step explanation:
From the question we are told that:
Diameter of vase [tex]d=6[/tex]
Number of marbles [tex]n_m=7[/tex]
Diameter of marbles [tex]d_m=3 inch[/tex]
Height of water [tex]h_w=12[/tex]
Generally the equation for Volume of water in cylindrical vase [tex]V_w[/tex] is mathematically given by
[tex]V_w= \pi r^2h - Volume \, of \, the\, balls[/tex]
Where Volume of the balls [tex]V_b[/tex] is
[tex]V_b= 7(4/3) \pi r^3\\\\V_b= 7(4/3) \pi (1.5)^3[/tex]
Therefore
[tex]V_w= \pi r^2h - Volume \, of \, the\, balls[/tex]
[tex]V_w= \pi (3)^2(12) - 8(4/3) \pi(1.5)^3[/tex]
The volume of the water in the vase is [tex]\pi 3^{2} (12) - 7 (4/3) \pi (1.5)^{3}[/tex].
It is given that,
Diameter of cylinder = 6 inches
Diameter of each marble = 3 inches
Number of marbles = 7
Height of the cylinder to the water level = 12 inches
The cylinder is a solid geometrical figure with straight parallel sides and a circular cross-section.
So, the volume of the water will be the difference in the volume of the cylinder to the water level and the sum of the volume of each marble.
The volume of water = [tex]\pi 3^{2} (12) - 7 (4/3) \pi (1.5)^{3}[/tex]
Therefore, the volume of the water is [tex]\pi 3^{2} (12) - 7 (4/3) \pi (1.5)^{3}[/tex].
To get more about cylinders visit:
https://brainly.com/question/9554871
