Four prisms

Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume?
a) 3000 cm2
b) 300 cm2
c) 3000 cm3
d) 300 cm3

Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The height of the prism is 5dm. What is the volume of the prism?
a) 20 250
b) 450
c) 40,500
d) 4,050

Question No.3: A regular square prism with a square base has a volume of 63 cm3 and a height of 7 cm. Calculate its surface.
a) 756
b) 102
c) 63
d) 414

Question No.4: Calculate the surface of a square prism high vh = 2 dm, the base of which is a trapezoid with bases z1 = 10cm, z2 = 8cm, height v = 4cm and with arms long r1 = r2 = 5cm.
a) 128 cm2
b) 596 cm2
c) 632 cm2
d) 532 cm2

Correct result:

V1 =  300 cm3
V2 =  30000 cm3
S3 =  102 cm2
S4 =  632 cm2

Solution:

a1=2.5 cm b1=100 mmcm=100/10 cm=10 cm c1=12 cm  V1=a1 b1 c1=2.5 10 12=300 cm3a_{1}=2.5 \ \text{cm} \ \\ b_{1}=100 \ mm \rightarrow cm=100 / 10 \ cm=10 \ cm \ \\ c_{1}=12 \ \text{cm} \ \\ \ \\ V_{1}=a_{1} \cdot \ b_{1} \cdot \ c_{1}=2.5 \cdot \ 10 \cdot \ 12=300 \ \text{cm}^3
a2=30 cm b2=20 cm c2=5 dmcm=5 10 cm=50 cm  V2=a2 b2 c2=30 20 50=30000 cm3a_{2}=30 \ \text{cm} \ \\ b_{2}=20 \ \text{cm} \ \\ c_{2}=5 \ dm \rightarrow cm=5 \cdot \ 10 \ cm=50 \ cm \ \\ \ \\ V_{2}=a_{2} \cdot \ b_{2} \cdot \ c_{2}=30 \cdot \ 20 \cdot \ 50=30000 \ \text{cm}^3
V3=63 cm3 c=7 cm  S1=V3/c=63/7=9 cm2 a=S1=9=3 cm  S3=4 a c+2 S1=4 3 7+2 9=102 cm2V_{3}=63 \ \text{cm}^3 \ \\ c=7 \ \text{cm} \ \\ \ \\ S_{1}=V_{3}/c=63/7=9 \ \text{cm}^2 \ \\ a=\sqrt{ S_{1} }=\sqrt{ 9 }=3 \ \text{cm} \ \\ \ \\ S_{3}=4 \cdot \ a \cdot \ c + 2 \cdot \ S_{1}=4 \cdot \ 3 \cdot \ 7 + 2 \cdot \ 9=102 \ \text{cm}^2
v4=2 dmcm=2 10 cm=20 cm z1=10 cm z2=8 cm v=4 cm r1=5 cm r2=5 cm  S44=z1+z22 v=10+82 4=36 cm2  S4=(z1+z2+r1+r2) v4+2 S44=(10+8+5+5) 20+2 36=632 cm2v_{4}=2 \ dm \rightarrow cm=2 \cdot \ 10 \ cm=20 \ cm \ \\ z_{1}=10 \ \text{cm} \ \\ z_{2}=8 \ \text{cm} \ \\ v=4 \ \text{cm} \ \\ r_{1}=5 \ \text{cm} \ \\ r_{2}=5 \ \text{cm} \ \\ \ \\ S_{44}=\dfrac{ z_{1}+z_{2} }{ 2 } \cdot \ v=\dfrac{ 10+8 }{ 2 } \cdot \ 4=36 \ \text{cm}^2 \ \\ \ \\ S_{4}=(z_{1}+z_{2}+r_{1}+r_{2}) \cdot \ v_{4} + 2 \cdot \ S_{44}=(10+8+5+5) \cdot \ 20 + 2 \cdot \ 36=632 \ \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!





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.

Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert area units?
Do you know the volume and unit volume, and want to convert volume units?

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Prism 4 sides
    kvader11_5 Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
  • Water tank
    cuboid_22 What is the height of the cuboid-shaped tank with the bottom dimensions of 80 cm and 50 cm if the 480 liters of water reaches 10 cm below the top?
  • Aquarium
    akvarko The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edg
  • Cage
    klietka-c.-6 How many m2 of mesh farmer use for fencing of a cuboid cage with dimensions 25m, 18m, and 2.5m?
  • Cardboard
    cuboid_14 How many m2 of cardboard are needed to make the cuboid with dimensions 40 cm 60 cm and 20 cm?
  • Basen
    bazen_9 How many square meters of tiles we need to tile the walls and floor of the pool 15 meters long, six meters wide and two meters?deep
  • Three-quarters of its volume
    bazen2 The pool has a block shape with a length of 8m, a width of 5.3m and a depth of 1.5m. How many hl of water is in it if it is filled to three-quarters of its volume?
  • Third dimension
    star_1 Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
  • Volume and surface area
    cuboid_2 Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
  • Surface and volume
    cuboid_2 Find the surface and volume of a cuboid whose dimensions are 1 m, 50 cm, and 6 dm.
  • Fire tank
    pool_3 How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?
  • Hectoliters
    hl How many hectoliters of water fits into cuboid tank with dimensions of a = 3.5 m b = 2.5 m c = 1.4 m?
  • The shop
    lahev The shop has 3 hectoliters of water. How many liter bottles is it?
  • Two cuboids
    cuboid_13 Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
  • Aquarium II
    akvarium_hranol Calculate how much glass we need to build an aquarium with a rectangular shape with base 70 cm × 70 cm and a height of 70 cm, if the waste is 2%. Aquarium haven't top glass.
  • Expression
    expr_2 Solve for a specified variable: P=a+4b+3c, for a
  • Rape
    repka The agricultural cooperative harvested 525 ares of rape, of which received 5.6 tons of rape seeds. Calculate the yield per hectare of rape.