Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.

Correct result:

S =  2335 cm2

#### Solution:

$D_{1}=28 \ \text{cm} \ \\ D_{2}=44 \ \text{cm} \ \\ \ \\ s=30 \ \text{cm} \ \\ q=1 + \dfrac{ 5 }{ 100 }=\dfrac{ 21 }{ 20 }=1.05 \ \\ \ \\ r_{1}=D_{1}/2=28/2=14 \ \text{cm} \ \\ r_{2}=D_{2}/2=44/2=22 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r_{2}^2 - \pi \cdot \ r_{1}^2=3.1416 \cdot \ 22^2 - 3.1416 \cdot \ 14^2 \doteq 904.7787 \ \text{cm}^2 \ \\ \ \\ S_{2}=\pi \cdot \ r_{1} \cdot \ s=3.1416 \cdot \ 14 \cdot \ 30 \doteq 1319.4689 \ \text{cm}^2 \ \\ \ \\ S=q \cdot \ (S_{1}+S_{2})=1.05 \cdot \ (904.7787+1319.4689)=2335 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Do you want to convert length units?
Do you want to round the number??

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• A bottle
A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh?
• Motorcycle engine
The motorcycle engine has a constant power of 1.2 kW for 0.5 hours. How much work does the engine do? Express work in kWh and Ws units.
• Three examples per-mille
A. Calculate 1.5 ‰ from 4.5 liters of blood. Express the result in milliliters. B. Calculate three ‰ from € 50,000. C. The tray they brought breakfast to the landlord's bed is made of an alloy that contains 830 ‰ of silver. How much silver did they use
• Bike cost
The father gave his son € 100 to buy a bicycle, which was 40% of the total amount of the bicycle. How much did the bike cost?
• Coordinates
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• Tournament
How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the overall winner of the tournament?
• Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
• Finite arithmetic sequence
How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?
• Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
• Cuboid edges
Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2: 3: 4 and the longest edge measures 10cm.
• Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
• The cable car
The cable car is 2610 m long and rises at an angle of 35°. Calculate the height difference between the lower and upper station of the cable car.
• Sailing
Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then she docked and launched the nets. How far was she from the pl
• Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
• Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
• Fighter
A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.