1. To find the height of the candle, we can use the formula for the volume of a cylinder: V = πr²h. Since the wick is located in the center, the radius is half of the diameter. We are given the volume of the wax used (289 cm³) and the distance of the wick to the edge (314 cm), so we can set up the following equations:
V = πr²h
289 = π(314/2)²h
289 = π(157)²h
289 = 24613πh
h ≈ 0.0117 cm
Therefore, the height of the candle is approximately 0.0117 cm.
2. The volume of the chocolate syrup in the saucepan can be calculated using the formula for the volume of a cylinder: V = πr²h. The volume of each jar can also be calculated using the same formula. To find the maximum number of jars Amanda can fill, we divide the volume of the saucepan by the volume of one jar:
Volume of saucepan = π(6)²(3) = 108π cubic inches
Volume of one jar = π(1.5)²(2.5) = 5.625π cubic inches
Maximum number of jars = 108π / 5.625π ≈ 19.2
Amanda can completely fill a maximum of 19 jars with the chocolate syrup.
3. The volume of a cube is given by the formula V = s³, where s is the length of one side. Since the cube has a height of 9 cm, all sides are equal and s = 9 cm. Therefore, the volume of Michelle's cube is:
V = 9³ = 729 cm³
Since Tasha's pyramid has the same base area and height as Michelle's cube, the base area of the pyramid is also 9 cm². The volume of a square-based pyramid is given by the formula V = (1/3)Bh, where B is the base area and h is the height. Therefore, the volume of Tasha's pyramid is:
V = (1/3)(9)(9) = 27 cm³
4. The rate of air leaking from the balloon is 28 cubic feet per minute, so the rate of decrease in volume of the balloon is 28 ft³/min. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Plugging in the values, we find:
V = (4/3)π(8)³ = 2144π ft³
To find the time it takes for the balloon to empty fully, we divide the volume of the balloon by the rate of air leaking:
2144π / 28 ≈ 241.8 minutes
Therefore, it would take approximately 241.8 minutes for the balloon to empty fully.
1. The distance of the wick to the edge of a cylindrical candle is 314
cm, and the volume of wax used in the candle is approximately 289 cm³. Assuming the wick is located in the center of the candle, find the height of the candle to the nearest tenth.
2. Amanda is making mini jars full of homemade chocholate syrup to give as party favors. She makes a big batch of chocolate syrup in a cylindrical saucepan. the diameter of the saucepan is 12 inches, and the syrip fills the pan to a height of 3 inches. The jars she plans to fill are cylindrical with a diameter of 3 inches and a height of 2.5 inches.
What is the maximum number of jars that Amanda can completely fill using the chocolate syrup? Show all your work and explain how you get your answer.
3. Michelle creates a cube with a height of 9 centimeters. Her friend Tasha creates a square-based pyramid with the same height and base area as Michelle’s cube. Find the volume of Michelle’s cube and use it to find the volume of Tasha’s pyramid. Show all work.
4. Air is leaking from a spherical-shaped advertising balloon at the rate of 28 cubic feet per minute. If the radius of the ball is 8 feet, how long would it take for the balloon to empty fully ? Round your answer to the nearest minute. Show all your work and explain how you get your answer.
1 answer
1 answer