The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.

Correct result:

V =  10.24 dm3
S =  31.383 dm2


a=24 cmdm=24/10 dm=2.4 dm b=3.2 dm h=0.4 mdm=0.4 10 dm=4 dm  S1=a b=2.4 3.2=19225=7.68 dm2  V=13 S1 h=13 7.68 4=25625=10.24 dm3a=24 \ cm \rightarrow dm=24 / 10 \ dm=2.4 \ dm \ \\ b=3.2 \ \text{dm} \ \\ h=0.4 \ m \rightarrow dm=0.4 \cdot \ 10 \ dm=4 \ dm \ \\ \ \\ S_{1}=a \cdot \ b=2.4 \cdot \ 3.2=\dfrac{ 192 }{ 25 }=7.68 \ \text{dm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 7.68 \cdot \ 4=\dfrac{ 256 }{ 25 }=10.24 \ \text{dm}^3
s2=h2+(a/2)2=42+(2.4/2)24.1761 dm s3=h2+(b/2)2=42+(3.2/2)24.3081 dm  S2=a s32=2.4 4.308125.1698 dm2 S3=b s22=3.2 4.176126.6818 dm2  S=S1+2 S2+2 S3=7.68+2 5.1698+2 6.6818=31.383 dm2s_{2}=\sqrt{ h^2 + (a/2)^2 }=\sqrt{ 4^2 + (2.4/2)^2 } \doteq 4.1761 \ \text{dm} \ \\ s_{3}=\sqrt{ h^2 + (b/2)^2 }=\sqrt{ 4^2 + (3.2/2)^2 } \doteq 4.3081 \ \text{dm} \ \\ \ \\ S_{2}=\dfrac{ a \cdot \ s_{3} }{ 2 }=\dfrac{ 2.4 \cdot \ 4.3081 }{ 2 } \doteq 5.1698 \ \text{dm}^2 \ \\ S_{3}=\dfrac{ b \cdot \ s_{2} }{ 2 }=\dfrac{ 3.2 \cdot \ 4.1761 }{ 2 } \doteq 6.6818 \ \text{dm}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2} + 2 \cdot \ S_{3}=7.68 + 2 \cdot \ 5.1698 + 2 \cdot \ 6.6818=31.383 \ \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...):

Showing 0 comments:
1st comment
Be the first to comment!

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

We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Two rectangular boxes
    cuboid_2 Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
  • A map
    land_1 A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?
  • Observation tower
    ship_1 From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower?
  • The copper wire
    cu_wire The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
  • A drone
    drone A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in
  • What percentage
    astronaut What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
  • Fighter
    vyskovy uhol 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.
  • Two trains
    trains_1 The train runs at speed v1 = 72 km/h. The passenger, sitting in the train, observed that a train long l = 75m in 3 s passed on the other track in the opposite direction. Calculate the speed of this train.
  • Squares ratio
    squares2 The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
  • Marlon
    meter Marlon drew a scale drawing of a summer camp. In real life, the sand volleyball court is 8 meters wide. It is 4 centimeters wide in the drawing. What is the drawing's scale factor? Simplify your answer and write it as a ratio, using a colon.
  • Cyclist 12
    cyclist What is the average speed of a cycle traveling at 20 km in 60 minutes in km/h?
  • My father
    plot2 My father cut 78 slats on the fence. The shortest of them was 97 cm long, the longer one was 102 cm long. What was the total length of the slats in cm?
  • Winch drum
    bubon Originally an empty winch drum with a diameter of 20 cm and a width of 30 cm on the rescue car, he started winding a rope with a thickness of 1 cm beautifully from edge to edge. The winch stopped after 80 turns. It remains to spin 3.54m of rope (without h
  • The swallow
    lastovicka The swallow will fly 2.8 km per minute. How many km will the swallow fly in one hour?
  • Self-oscillation period
    lambda The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s.
  • Rotaty motion
    rotaryMotion What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
  • Newtonmeters
    kluc-skrutky The driver loosened the nut on the car wheel with a wrench that held 20 cm from the axis of the bolt. He acted on the key with a force of 320N. At what moment did he act on the bolt?