Question 434.
A solid has an isosceles triangular base of side length 10, 13, 13 inches. Cross sections parallel to one of the two equal length sides are equilateral triangles. Find the volume of the solid with the exact value.
Answer 434.
Let in ΔABC,
AB = AC = 13 and BC = 10
Consider a small length DD' on BC and EE' on AC such that DE and D'E' are parallel to AB
Let BD = x and DD' = dx
=> DE = x * (13/10)
=> Area of equilateral triangle of length DE
= (1/2) (13x/10)^2 sin60° = x * 13√3/40
and volume of the thin slice of width DD'
dV = (13√3/40) ∫ x dx ... (x=0 to 10)
=> V = (13√3/80) x^2 ... (x=0 to 10)
=> V = 65√3/4 cubic units.
Link to YA!
A solid has an isosceles triangular base of side length 10, 13, 13 inches. Cross sections parallel to one of the two equal length sides are equilateral triangles. Find the volume of the solid with the exact value.
Answer 434.
Let in ΔABC,
AB = AC = 13 and BC = 10
Consider a small length DD' on BC and EE' on AC such that DE and D'E' are parallel to AB
Let BD = x and DD' = dx
=> DE = x * (13/10)
=> Area of equilateral triangle of length DE
= (1/2) (13x/10)^2 sin60° = x * 13√3/40
and volume of the thin slice of width DD'
dV = (13√3/40) ∫ x dx ... (x=0 to 10)
=> V = (13√3/80) x^2 ... (x=0 to 10)
=> V = 65√3/4 cubic units.
Link to YA!
No comments:
Post a Comment