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

Result

S =  66 cm²
V =  0.036 l

Solution:

$a=3 \ \text{cm} \ \\ u=5 \ \text{cm} \ \\ \ \\ c=\sqrt{ u^2-a^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ \ \\ S_{1}=a^2=3^2=9 \ \text{cm}^2 \ \\ \ \\ S_{2}=4 \cdot \ a \cdot \ c=4 \cdot \ 3 \cdot \ 4=48 \ \text{cm}^2 \ \\ \ \\ S=2 \cdot \ S_{1} + S_{2}=2 \cdot \ 9 + 48=66 \ \text{cm}^2$

$V_{1}=S_{1} \cdot \ c=9 \cdot \ 4=36 \ \text{cm}^3 \ \\ V=V_{1} \rightarrow l=V_{1} / 1000 \ l=0.036 \ l=\dfrac{ 9 }{ 250 }=0.036 \ \text{l}$

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Quadrangular prism
   Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
2. Triangular prism
   Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
3. Square diagonal
   Calculate the length of diagonal of the square with side a = 23 cm.
4. Tree trunk
   From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
5. Castle model
   The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm² of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of wo
6. Cylinder surface area
   Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm³. Calculate its surface area.
7. Cone area and side
   Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
8. Ice cream in cone
   In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
9. Digging
   A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ?
10. Diagonals in diamons/rhombus
    Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
11. Satin
    Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
12. Tv screen
    The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
13. Center of the cube
    Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
14. Cube volume
    The cube has a surface of 384 cm². Calculate its volume.
15. Water well
    Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
16. Chord circle
    The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
17. Double ladder
    The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?