# 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:

$(a+5)^3=a^3+485 \ \\ a^3 + 15 \ a^2 + 75 \ a + 125=a^3+485=3^3+485=488 \ \\ \ \\ \ \\ 15 a^2 + 75 a + 125=485 \ \\ \ \\ 15 \ a^2 + 75 \ a + 125=485 \ \\ 15a^2 +75a -360=0 \ \\ \ \\ p=15; q=75; r=-360 \ \\ D=q^2 - 4pr=75^2 - 4\cdot 15 \cdot (-360)=27225 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ -75 \pm \sqrt{ 27225 } }{ 30 } \ \\ a_{1,2}=\dfrac{ -75 \pm 165 }{ 30 } \ \\ a_{1,2}=-2.5 \pm 5.5 \ \\ a_{1}=3 \ \\ a_{2}=-8 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 15 (a -3) (a +8)=0 \ \\ a=a_{1}=3 \ \\ \ \\ S_{1}=6 \cdot \ a^2=6 \cdot \ 3^2=54 \ \text{cm}^2$

Checkout calculation with our calculator of quadratic equations.

$S_{2}=6 \cdot \ (a+5)^2=6 \cdot \ (3+5)^2=384 \ \text{cm}^2$

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!

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

Be the first to comment!

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.

## Next similar math problems:

1. Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
2. Cube 6
Volume of the cube is 216 cm3, calculate its surface area.
3. Balls
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
4. Rate or interest
At what rate percent will Rs.2000 amount to Rs.2315.25 in 3 years at compound interest?
5. Three members GP
The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
6. Short cut
Imagine that you are going to the friend. That path has a length 120 meters. Then turn doprava and go another 630 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
7. Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
8. Hens
11 hens will eat spilled grain from 6AM to 16 PM. At 11 hour grandmother brought 4 hens from the neighbors. At what time was grain out?
9. Root
The root of the equation ? is: ?
10. Evaluate - order of ops
Evaluate the expression: 32+2[5×(24-6)]-48÷24 Pay attention to the order of operation including integers
11. The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
12. Precious metals
In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3