Cuboid and eq2

Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.

Correct answer:

V =  18.2904 cm3

Step-by-step explanation:

h=6 cm S=48 cm2 S=4ah+2a2 48=46a+2a2  48=4 6 a+2 a2 2a224a+48=0 2a2+24a48=0  p=2;q=24;r=48 D=q24pr=24242(48)=960 D>0  a1,2=q±D2p=24±9604=24±8154 a1,2=6±7.74596669241 a1=1.74596669241 a2=13.7459666924   Factored form of the equation:  2(a1.74596669241)(a+13.7459666924)=0  a=a1=1.7461.746  V=a2 h=1.7462 618.2904=18.2904 cm3   Verifying Solution:  S2=4 a h+2 a2=4 1.746 6+2 1.7462=48 cm2 S2=S

Our quadratic equation calculator calculates it.

We will be pleased if You send us any improvements to this math problem. Thank you!


Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.

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

Related math problems and questions:

  • Uboid volume
    cuboid Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
  • Hexagonal prism 2
    hranol6b The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
  • Cuboid surface
    cuboid Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.
  • Surface of cuboid
    kvader11 Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
  • Truncated pyramid
    truncated_pyramid The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm2 greater than the upper base's content. Calculate the area of the upper base.
  • Triangular prism
    prism3 The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
  • Cuboid walls
    cuboid If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
  • Prism height
    prism_rt What is the prism's height with the base of a right triangle of 6 cm and 9 cm? The diaphragm is 10.8 cm long. The volume of the prism is 58 cm3. Calculate its surface.
  • Cube walls
    krychle Find the volume and surface area of the cube if the area of one wall is 40cm2.
  • Rhombus base
    paral_prism Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 15 cm. Prism height is twice the base edge length.
  • Four prisms
    hranol4b 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 prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t
  • Ratio-cuboid
    hranol222 The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
  • Cuboid - volume and areas
    cuboid The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
  • Solid cuboid
    cuboid A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
  • Quadrangular prism
    trapezium_prism The quadrangular prism has a volume of 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
  • Square prism
    lichob Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
  • Glass
    pohgar How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?