An icicle is in the shape of an inverted cone with a diameter of 14 mm and a height of 60 mm. How much frozen water is in the icicle? Use 3.14 for Pi. Round the answer to the nearest tenth.
188.4 millimeters cubed
980.0 millimeters cubed
3,077.2 millimeters cubed
9,231.6 millimeters cubed
To find the volume of the icicle, we can use the formula for the volume of a cone, which is given by:
V = (1/3)πr^2h
Where V is the volume, π is the value of Pi, r is the radius, and h is the height.
First, we need to find the radius of the icicle. Since the diameter is given as 14 mm, the radius is half of that, which is 7 mm.
Substituting the values into the formula, we get:
V = (1/3)(3.14)(7^2)(60)
= 3.14 * (49)(60)
= 3.14 * 2940
≈ 9,231.6 mm^3
Therefore, the frozen water in the icicle is approximately 9,231.6 millimeters cubed.
An icicle is in the shape of an inverted cone with a diameter of 9 mm and a height of 120 mm. The icicle drips at a rate of 75 millimeters cubed per minute. How long will it take the icicle to completely melt? Use 3.14 for Pi. Round the answer to the nearest tenth.
5.1 minutes
7.5 minutes
15.1 minutes
33.9 minutes
To find the time it takes for the icicle to completely melt, we need to find the volume of the icicle and divide it by the rate at which it is dripping.
The volume of the icicle can be calculated using the formula for the volume of a cone, which is given by:
V = (1/3)πr^2h
Where V is the volume, π is the value of Pi, r is the radius, and h is the height.
First, we need to find the radius of the icicle. Since the diameter is given as 9 mm, the radius is half of that, which is 4.5 mm.
Substituting the values into the formula, we get:
V = (1/3)(3.14)(4.5^2)(120)
= 3.14 * (20.25)(120)
= 3.14 * 2430
≈ 7636.2 mm^3
Next, we need to divide the volume of the icicle by the rate at which it is dripping, which is 75 mm^3 per minute:
Time = Volume / Rate
= 7636.2 mm^3 / 75 mm^3 per min
≈ 101.8 min
Therefore, it will take approximately 101.8 minutes for the icicle to completely melt. Rounded to the nearest tenth, it is approximately 101.8 minutes.
try aagain your incorrect
I apologize for the error. Let's try solving the problem again.
The volume of the icicle can be calculated using the formula for the volume of a cone, which is given by:
V = (1/3)πr^2h
Where V is the volume, π is the value of Pi, r is the radius, and h is the height.
First, we need to find the radius of the icicle. Since the diameter is given as 9 mm, the radius is half of that, which is 4.5 mm.
Substituting the values into the formula, we get:
V = (1/3)(3.14)(4.5^2)(120)
= (1/3)(3.14)(20.25)(120)
= 1509.5 mm³
Now, we divide the volume of the icicle by the rate at which it is dripping, which is 75 mm³ per minute:
Time = Volume / Rate
= 1509.5 mm³ / 75 mm³ per min
= 20.1266 min
Rounded to the nearest tenth, it will take approximately 20.1 minutes for the icicle to completely melt.
Therefore, the correct answer is 20.1 minutes.
What is the height of a cylinder with a volume of 936 pi cubic inches and a diameter of 24 inches?
1.625 inches
4.75 inches
6.5 inches
39 inches
The volume formula for a cylinder is given by:
V = πr^2h
Where V is the volume, π is the value of Pi, r is the radius, and h is the height.
We are given that the volume is 936π cubic inches and the diameter is 24 inches. To find the radius, we divide the diameter by 2:
r = 24 inches / 2 = 12 inches
Now we can substitute the values into the volume formula:
936π = π(12^2)h
936 = 144h
h = 936 / 144
h ≈ 6.5 inches
Therefore, the height of the cylinder is approximately 6.5 inches.