An icicle is in the shape of an inverted cone with a diameter of 9 mm and a height of 27 mm. In cubic millimeters, how much frozen water is in the icicle? Use 3.14 for Pi. Round your answer to the nearest hundredth.
The radius of the base of the cone is half of the diameter, so the radius is 9 mm / 2 = <<9/2=4.5>>4.5 mm
To find the volume of the ice in the icicle, we need to find the volume of the entire cone and subtract the volume of the hollow space inside the icicle.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
The volume of the entire cone is (1/3)(3.14)(4.5^2)(27) = 637.54 cubic millimeters
The volume of the hollow space inside the icicle is the same as the volume of a cone with a radius of 0. Since the radius is 0, the volume is 0.
So the total volume of frozen water in the icicle is 637.54 cubic millimeters - 0 cubic millimeters = 637.54 cubic millimeters.
Rounding to the nearest hundredth, we can say that there are approximately 637.54 cubic millimeters of frozen water in the icicle.
The volume of a cone is 108 pi cubic inches. Its height is 4 inches. What is the radius of the cone? Round the answer to the nearest tenth if necessary.
5.2 in.
9 in.
34.7 in.
81 in.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cone is 108π cubic inches and the height is 4 inches.
Substituting these values into the formula, we have 108π = (1/3)πr^2(4).
Cancelling out the common factor of π, we have 108 = (1/3)r^2(4).
Dividing both sides by (1/3)(4), we have 108 = r^2.
Taking the square root of both sides, we have r = √108.
Finding the square root of 108, we have r ≈ 10.39 inches.
Rounding this to the nearest tenth, we have r ≈ 10.4 inches.
Therefore, the radius of the cone is approximately 10.4 inches.
try again
We are given that the volume of the cone is 108π cubic inches and the height is 4 inches.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Substituting the given values into the formula, we have 108π = (1/3)πr^2(4).
Cancelling out the common factor of π, we have 108 = (1/3)r^2(4).
Dividing both sides by (1/3)(4), we have 108 = r^2.
Taking the square root of both sides, we have r = √108.
Finding the square root of 108, we have r ≈ 10.39 inches.
Rounding this to the nearest tenth, we have r ≈ 10.4 inches.
Therefore, the radius of the cone is approximately 10.4 inches.
The volume of a cone is 164 pi cubic feet. Its height is 12 feet. Ashlyn is finding the area of the base of the cone. Her work is shown below.
V = one-third B h. Step 1: 164 pi = one-third pi B (12). Step 2: 164 pi = 4 pi B. Step 3: StartFraction 164 pi Over 4 pi EndFraction = B. Step 4: 41 = B.
What is Ashlyn’s error?
In step 3, Ashlyn did not subtract 4 pi from 164 pi.
In step 2, Ashlyn did not find the correct value for multiplying One-third and 12.
In step 1, Ashlyn included a factor of Pi on the right side of the formula.
In step 1, Ashlyn did not substitute the correct value for the height in the formula.
Mark this and return
Ashlyn's error is in step 3 where she mistakenly simplified (164 pi) / (4 pi) = B to 41 = B.
To simplify (164 pi) / (4 pi), we can cancel out the common factor of pi and divide 164 by 4.
(164 pi) / (4 pi) = 41.
So the correct value for B is 41, which is what Ashlyn obtained, but she made an incorrect step by trying to cancel out the pi.
Therefore, the correct answer is: In step 3, Ashlyn did not correctly simplify the equation to obtain the correct value for B. She should have simplified (164 pi) / (4 pi) correctly to get B = 41.
Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Which statements about the green candle are true? Check all that apply. Use 3.14 for Pi.
The volume of the green candle is about 23.55 inches cubed.
The volume of the green candle is about 58.88 inches cubed.
The diameter of the green candle is 5 in.
The diameter of the green candle is 1.25 in.
The base area of the green candle is about 19.63 inches squared.
The base area of the green candle is about 7.85 inches squared.
The price of one green candle is about $5.89.
The price of one green candle is about $14.72.
To determine which statements are true, let's calculate the volume, diameter, base area, and price of the green candle.
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Substituting the given values, we have:
V = (1/3)(3.14)(2.5^2)(9)
= 23.5625 cubic inches (approx.)
So, the volume of the green candle is about 23.56 cubic inches.
The diameter of a cone is twice the radius, so the diameter is 2(2.5) = 5 inches.
Therefore, the statement "The diameter of the green candle is 5 inches" is true.
The formula for the base area of a cone is A = πr^2, where A is the base area and r is the radius.
Substituting the given radius, we have:
A = 3.14(2.5^2)
= 19.625 square inches (approx.)
So, the base area of the green candle is about 19.63 square inches.
The price of one green candle is $0.25 per cubic inch, and the volume of the green candle is 23.5625 cubic inches. Multiplying these values, we get:
Price = $0.25 × 23.5625
= $5.9 (approx.)
So, the price of one green candle is about $5.89.
Therefore, the true statements are:
- The volume of the green candle is about 23.55 inches cubed.
- The diameter of the green candle is 5 in.
- The base area of the green candle is about 19.63 inches squared.
- The price of one green candle is about $5.89.
The volume of a cone is 16 pi cubic inches. Its height is 12 inches. What is the radius of the cone?
2 in.
4 in.
12 in.
16 in.