# Prism 4 sides

The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters

Correct result:

S =  66 cm2
V =  0.036 l

#### Solution:

$a=3 \ \text{cm} \ \\ u=5 \ \text{cm} \ \\ \ \\ c=\sqrt{ u^2-a^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ \ \\ S_{1}=a^2=3^2=9 \ \text{cm}^2 \ \\ \ \\ S_{2}=4 \cdot \ a \cdot \ c=4 \cdot \ 3 \cdot \ 4=48 \ \text{cm}^2 \ \\ \ \\ S=2 \cdot \ S_{1} + S_{2}=2 \cdot \ 9 + 48=66 \ \text{cm}^2$
$V_{1}=S_{1} \cdot \ c=9 \cdot \ 4=36 \ \text{cm}^3 \ \\ V=V_{1} \rightarrow l=V_{1} / 1000 \ l=36 / 1000 \ l=0.036 \ l=\dfrac{ 9 }{ 250 }=0.036 \ \text{l}$

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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Do you know the volume and unit volume, and want to convert volume units?
Pythagorean theorem is the base for the right triangle calculator.

#### 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:

Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m2, length of the base edge a = 14 dm, height of the prism 1,500 mm.
• Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
• Alcohol from potatoes
In the distillery, 10 hl of alcohol can make from 8 t of potatoes. The rectangular field with dimensions of 600 m and 200 m had a yield of 20 t of potatoes per hectare. How many square meters of area are potatoes grown to obtain one liter of alcohol?
• The plan
The plan of the housing estate is in three scales 1: 5000,1: 10000,1: 15000. The distance between two points on a plan with a scale of 1: 10000 is 12 cm. What is this distance on the other two plans? What is this distance?
• Copper Cu wire
Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
• Central angle
What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
• The water tank
The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
• AL wire
What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.
• Telegraph poles
The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´?
• Aquarium height
How high does the water in the aquarium reach, if there are 36 liters of water in it? The length of the aquarium is 60 cm and the width is 4 dm.
• 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.
• Cyclist 12
What is the average speed of a cycle traveling at 20 km in 60 minutes in km/h?
• Concrete hatch
The concrete hatch for a round well has a diameter of 1300 mm and a thickness of 80 mm. Determine its weight in kg if the density of the concrete is 2545 kg/m3
• 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 on
• Surface and volume
Find the surface and volume of a cuboid whose dimensions are 1 m, 50 cm, and 6 dm.
• Water mixing
We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?