# Surface of the cylinder

Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.

Result

S =  70.053 dm2

#### Solution:

$V = 45 \ l = \pi r^2 h \ \\ 2 \pi r = 3 h \ \\ h = \dfrac23 \pi r \ \\ V = \dfrac23 \pi^2r^3 \ \\ r = \sqrt[3]{\dfrac{ 3V}{ 2 \pi^2}} = 1.9 \ dm \ \\ h = \dfrac23 \pi r = 3.98 \ dm \ \\ S = 2 \pi r^2 + 2\pi r h = 2 \pi \cdot 1.9^2 + 2\pi \cdot 1.9 \cdot 3.98 = 70.053 \ \text{dm}^2$

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 know the volume and unit volume, and want to convert volume units?

## Next similar math problems:

1. Cylinder surface, volume
The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
2. Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
3. Cylinder - area
The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
4. Rotary cylinder 2
Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm3?
5. Cylinder - A&V
The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
6. Cylinder diameter
The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?
7. Calculate 3
Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
8. Jar
From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
9. Conserving water
Calculate how many euros are spent annually on unnecessary domestic hot water, which cools during the night in pipeline. Residential house has 129 m of hot water pipelines 5/8" and the hot water has a price of 7 Eur/m3.
10. Circular pool
The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
11. Water flow
How much water flow in pipe with a diameter of 16 cm in 1 hour if the water velocity is 2.5 m/s?
12. Water well
Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
13. Conva
How many liters of water fit into the shape of a cylinder with a bottom diameter 20 cm and a height 45 cm?
14. Plasticine ball
Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls
15. Cylindrical tank 2
If a cylindrical tank with volume is used 12320cm raised to the power of 3 and base 28cm is used to store water. How many liters of water can it hold?
16. Gasoline canisters
35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canist
17. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?