Hollow sphere

The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?

Correct result:

r =  8 cm

Solution:

V=3432 cm3 h=3 cm V=V1V2 V1=4/3π (r+h)3 V2=4/3π r3 3/4/π V=(r+h)3r3 k=3/4/π V=3/4/3.1416 3432819.3296 9r2+27r+27=819.3296  9r2+27r792.33=0  a=9;b=27;c=792.33 D=b24ac=27249(792.33)=29252.8656 D>0  r1,2=b±D2a=27±29252.8718 r1,2=1.5±9.5019272898829 r1=8.0019272898829 r2=11.001927289883   Factored form of the equation:  9(r8.0019272898829)(r+11.001927289883)=0 r>0 r=[r1]=[8.0019]=8 cm V1=4/3π (r+h)3=4/3 3.1416 (8+3)35575.2798 V2=4/3π r3=4/3 3.1416 832144.6606 V3=V1V2=5575.27982144.66063430.6192V=3432 \ \text{cm}^3 \ \\ h=3 \ \text{cm} \ \\ V=V_{1} - V_{2} \ \\ V_{1}=4/3 \pi \cdot \ (r+h)^3 \ \\ V_{2}=4/3 \pi \cdot \ r^3 \ \\ 3/4/\pi \cdot \ V=(r+h)^3 - r^3 \ \\ k=3/4/\pi \cdot \ V=3/4/3.1416 \cdot \ 3432 \doteq 819.3296 \ \\ 9r^2+27r +27=819.3296 \ \\ \ \\ 9r^2 +27r -792.33=0 \ \\ \ \\ a=9; b=27; c=-792.33 \ \\ D=b^2 - 4ac=27^2 - 4\cdot 9 \cdot (-792.33)=29252.8656 \ \\ D>0 \ \\ \ \\ r_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ -27 \pm \sqrt{ 29252.87 } }{ 18 } \ \\ r_{1,2}=-1.5 \pm 9.5019272898829 \ \\ r_{1}=8.0019272898829 \ \\ r_{2}=-11.001927289883 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 9 (r -8.0019272898829) (r +11.001927289883)=0 \ \\ r>0 \ \\ r=[ { r_{1} } ]=[ { 8.0019 } ]=8 \ \text{cm} \ \\ V_{1}=4/3 \pi \cdot \ (r+h)^3=4/3 \cdot \ 3.1416 \cdot \ (8+3)^3 \doteq 5575.2798 \ \\ V_{2}=4/3 \pi \cdot \ r^3=4/3 \cdot \ 3.1416 \cdot \ 8^3 \doteq 2144.6606 \ \\ V_{3}=V_{1}-V_{2}=5575.2798-2144.6606 \doteq 3430.6192

Checkout calculation with our calculator of quadratic equations.




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 have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

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


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

Next similar math problems:

  • Cube corners
    polyhedra-truncated-cube From cube of edge 5 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?
  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  • Adding percentages
    percent 55%+36%+88%+71%+100=63% what is whole (X)? Percents can be added directly together if they are taken from the same whole, which means they have the same base amount. .. . You would add the two percentages to find the total amount.
  • 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
  • Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  • Fifth member
    arithmet_seq_1 Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
  • Determine AP
    diff Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
  • Difference AP 4
    sequence_geo_1 Calculate the difference of the AP if a1 = 0.5, a2 + a3 = -1.1
  • Crystal water
    laboratory The chemist wanted to check the content of water of crystallization of chromic potassium alum K2SO4 * Cr2 (SO4) 3 * 24 H2O, which was a long time in the laboratory. From 96.8 g of K2SO4 * Cr2 (SO4) 3 * 24 H2O prepared 979 cm3 solution of base.
  • Equation
    cubic How many real roots has equation ? ?
  • Expression with powers
    eq222_9 If x-1/x=5, find the value of x4+1/x4
  • Stones 3
    stones Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
  • Children
    children_3 The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
  • Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  • Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8
  • Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  • Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3