The block

The block, the edges formed by three consecutive GP members, has a surface area of 112 cm2. The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block.

Correct answer:

V =  64 cm3

Step-by-step explanation:

b= qa c = qa2 S=112 cm2  S = 2(ab+bc+ca) = 2(q a2 + q3a2 + q2a2) S = 2a2(q+q2+q3)  a+b+c=14 a+aq+aq2 = 14 a(1+q+q2)=14 a(q+q2+q3)=14q  S = 2a2(q+q2+q3) = 2a2 14q/a = 2 14 a q   b = aq b=2 14S=2 14112=4 cm  S = 2(b/q b + b q b + b q b/q)  S = 2(b2/q + b2 q + b2) S/2/b2 = 1/q+q+1  q S/2/b2=1+q2+q  q 112/2/42=1+q2+q q2+2.5q1=0 q22.5q+1=0  a=1;b=2.5;c=1 D=b24ac=2.52411=2.25 D>0  q1,2=2ab±D=22.5±2.25 q1,2=1.25±0.75 q1=2 q2=0.5 q=2  a=b/q=4/2=2 c=q b=2 4=8  V=a b c=2 4 8=64=64 cm3   Verifying Solution:  S1=2 (a b+b c+c a)=2 (2 4+4 8+8 2)=112 cm2 s1=a+b+c=2+4+8=14 cm

Our quadratic equation calculator calculates it.




Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Do you have a system of equations and looking for calculator system of linear equations?
Tip: Our volume units converter will help you convert volume units.

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

Related math problems and questions: