The Crayola crayon shown below has a radius of 2 mm how much wax is needed to make the crayon use 3.14 for pi and round your answer to the nearest whole number the height of the crayon is 9 mm for the bottom and the tip is 6 mm
To find the volume of the crayon, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Given r = 2 mm and h = 9 mm, we can substitute these values into the formula:
V = π(2 mm)^2(9 mm)
V = π(4 mm^2)(9 mm)
V = π(36 mm^3)
Using the value π = 3.14 (as given in the question), we can find the volume: V = 3.14(36 mm^3)
V ≈ 113.04 mm^3
Since we are dealing with wax, we can assume that it has a similar density to water, which is approximately 1 g/cm^3. Therefore, the volume of the wax (in milliliters) is equal to the mass (in grams).
So, the wax needed to make the crayon is approximately 113.04 milliliters.
Rounding this to the nearest whole number, the wax needed is 113 grams.
I don't think the answer is right they're two heights for the crayon 9 mm for round cylinder and 6 mm for the tip which is like a cone
Apologies for the confusion. Let's calculate the volume of the crayon considering it consists of two sections: a cylindrical body and a conical tip.
Volume of the cylindrical body:
V_cylinder = πr^2h_cylinder
Given the radius, r = 2 mm, and the height of the cylindrical body, h_cylinder = 9 mm, we can calculate:
V_cylinder = 3.14 * (2 mm)^2 * 9 mm
V_cylinder ≈ 113.04 mm^3
Volume of the conical tip:
V_cone = (1/3) * πr^2h_cone
Given the radius, r = 2 mm, and the height of the conical tip, h_cone = 6 mm, we can calculate:
V_cone = (1/3) * 3.14 * (2 mm)^2 * 6 mm
V_cone ≈ 25.12 mm^3
Total volume of the crayon:
V_total = V_cylinder + V_cone
V_total = 113.04 mm^3 + 25.12 mm^3
V_total ≈ 138.16 mm^3
Since we assume the wax density is approximately 1 g/cm^3, the volume of the wax needed is approximately 138.16 grams. Rounding this to the nearest whole number, the amount of wax needed to make the crayon is 138 grams.
If the height of a cone is 20 yd and the volume is 3014.4 what is the radius use 3.14 to solve and remember to show your work
To find the radius of the cone, we can use the formula for the volume of a cone: V = (1/3) * π * r^2 * h, where V is the volume, r is the radius, and h is the height.
Given V = 3014.4 and h = 20, we can substitute these values into the formula:
3014.4 = (1/3) * 3.14 * r^2 * 20
Divide both sides of the equation by (1/3) * 3.14 * 20:
3014.4 / ((1/3) * 3.14 * 20) = r^2
3014.4 / (0.52333333333) = r^2
5751.7 = r^2
To find the radius, we need to take the square root of both sides:
sqrt(5751.7) = sqrt(r^2)
r ≈ 75.85
Rounding to the nearest whole number, the radius of the cone is approximately 76 yards.
Can you show the work a little simpler
Apologies for any confusion. Let's simplify the work to find the radius of the cone.
We have the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given V = 3014.4 and h = 20, we can substitute these values into the formula:
3014.4 = (1/3) * 3.14 * r^2 * 20
Remove the fraction and simplify:
3014.4 = (3.14/3) * r^2 * 20
3014.4 = r^2 * 6.28 * 20
Divide both sides of the equation by 6.28 * 20:
3014.4 / (6.28 * 20) = r^2
3014.4 / 125.6 ≈ r^2
24 ≈ r^2
To find the radius, we need to take the square root of both sides:
√24 ≈ √r^2
r ≈ √24
Using a calculator or approximating, r ≈ 4.9
Rounding to the nearest whole number, the radius of the cone is approximately 5 yards.