Magnified cube

If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.

Result

S1 =  54 cm2
S2 =  384 cm2

Solution:

(a+5)3=a3+485 a3+15 a2+75 a+125=a3+485=33+485=488   15a2+75a+125=485  15 a2+75 a+125=485 15a2+75a−360=0  p=15;q=75;r=−360 D=q2−4pr=752−4⋅15⋅(−360)=27225 D>0  a1,2=−q±D2p=−75±2722530 a1,2=−75±16530 a1,2=−2.5±5.5 a1=3 a2=−8   Factored form of the equation:  15(a−3)(a+8)=0 a=a1=3  S1=6⋅ a2=6⋅ 32=54 cm2(a+5)^3=a^3+485 \ \\ a^3 + 15 \ a^2 + 75 \ a + 125=a^3+485=3^3+485=488 \ \\ \ \\ \ \\ 15 a^2 + 75 a + 125=485 \ \\ \ \\ 15 \ a^2 + 75 \ a + 125=485 \ \\ 15a^2 +75a -360=0 \ \\ \ \\ p=15; q=75; r=-360 \ \\ D=q^2 - 4pr=75^2 - 4\cdot 15 \cdot (-360)=27225 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ -75 \pm \sqrt{ 27225 } }{ 30 } \ \\ a_{1,2}=\dfrac{ -75 \pm 165 }{ 30 } \ \\ a_{1,2}=-2.5 \pm 5.5 \ \\ a_{1}=3 \ \\ a_{2}=-8 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 15 (a -3) (a +8)=0 \ \\ a=a_{1}=3 \ \\ \ \\ S_{1}=6 \cdot \ a^2=6 \cdot \ 3^2=54 \ \text{cm}^2

Checkout calculation with our calculator of quadratic equations.

S2=6⋅ (a+5)2=6⋅ (3+5)2=384 cm2S_{2}=6 \cdot \ (a+5)^2=6 \cdot \ (3+5)^2=384 \ \text{cm}^2

Try another example


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!
avatar




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 quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  1. Cube corners
    polyhedra-truncated-cube From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
  2. Cubes - diff
    cube_2 Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
  3. Calculate 3
    cube_sphere_in_1 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
  4. Cube volume
    cube6 The cube has a surface of 384 cm2. Calculate its volume.
  5. Swimming pool
    basen The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
  6. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  7. Product
    floring The product of two consecutive odd numbers is 8463. What are this numbers?
  8. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  9. Calculation
    pocty How much is sum of square root of six and the square root of 225?
  10. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  11. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  12. The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  13. Quadratic equation
    parabola_1 Solve quadratic equation: 2x2-58x+396=0
  14. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  15. Birthdays
    bonbons_1 In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
  16. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  17. Apples
    apples_5 A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?