To solve this problem, the first thing we have to do is find the volume of the inside of each glass.
Glass 1 is a cylinder with a height of 6 cm and a radius of 3 cm (6 cm / 2).
The formula for finding the volume of a cylinder is V = πr²h; where r is the radius and h is the height. First, assign values to the variables (I will use 3.14 for pi).
π = 3.14
r = 3
h = 6
Then, just substitute into the equation and solve.
V = πr²h
V ≈ (3.14)(3²)(6)
V ≈ (3.14)(9)(6)
V ≈ 169.56 cm³
I use the "≈" symbol to indicate that the answer is not exact due to me rounding pi. Let me know if you need to know the exact volume.
Glass 2 can be separated into both a cylinder and a half circle to make it easier to solve. The cylinder is 3 inches high with a radius of 3 cm.
V ≈ πr²h
V ≈ (3.14)(3²)(3)
V ≈ (3.14)(9)(3)
V ≈ 84.78 cm³
The formula for finding the volume of a half-circle (or half-<em>sphere</em>, I should say) is V = (4/3 πr³) / 2. The half-sphere has a radius of 3 cm and a height of 3 cm.
V = (4/3)(3.14)(3³) / 2
V ≈ 113.04 / 2
V ≈ 56.52 cm³
Then just add the two volumes together to get the volume of the whole glass.
84.78 + 56.52 = 141.3
V ≈ 141.3 cm³
Glass 3 is a cone. The volume for finding the volume of a cone is
V = πr²(h/2)
Before we can solve for the volume, though, we first need to find the height. This is a right cone, meaning that a straight line running from the center of its base to its tip forms a right angle with the base. This allows use to use the Pythagorean Theorem to find h using the radius and the lateral height.
a² + b² = c²
3² + b² = 7²
9 + b² = 49
9 + b² - 9 = 49 - 9
b² = 40
√b² = √40
b ≈ 6.32
V ≈ (3.14)(3²)(6.32 / 3)
V ≈ (28.26)(≈2.11)
V ≈ 59.6286 cm³
Two more steps to go...
Now, we have to find the volume of a single ice cube.
V = (4/3)πr³
V ≈ (4/3)(3.14)(1³)
V ≈ 4.19 cm³
Finally, to finish solving the problem, we have to find out how many ice cubes can fit inside each glass. To do this, we just divide the volume of the glass by the volume of the ice cube.
Glass 1
169.56 / 4.19 ≈ 40.47 or just 40.
Glass 2
141.3 / 4.19 ≈ 33.72 or 34.
Glass 3
59.6286 / 4.19 ≈ 11.84 or 12.
I know it's kinda long and the answer's might not match up exactly with the ones you were supposed to give, but I hope it helps all the same!
And if you want to know the exact volumes (in terms of pi instead of 3.14 for pi), just let me know and I can get that for you.
