A cylinder has a height of 10cm and a radius of 4cm.
The volume of the cylinder is 503 cm^3.
The length of a pencil is 13cm.
The pencil cannot be broken.
Show that this pencil cannot fit inside the cylinder.
2006-12-02 22:17:44 · 3 answers · asked by mbchelsea 1 in Science & Mathematics ➔ Mathematics
To answer this question, volume of the cylinder is not required.
The cross section of the cylinder will look like a rectangle
this rectangle's height is 10 cm (height of the cylinder)
this rectangle's width is 8 cm (4x2 - 8; 2 times the radius)
If the pencil has to fit into this area, it should NOT be longer than the diagonal of this cylinder.
So the diagonal of this cylinder can be found by Pythagorean formula
Diagonal^2 = 10^2 + 8^2
Diagonal = SquareRoot (164)
Diagonal approximately = 12.81 cm, which is smaller than 13 cm;
therfore you cannot possibly fit the pencil in there.
2006-12-02 22:26:07 · answer #1 · answered by mahindraoye 2 · 0⤊ 0⤋
The "diagonal" of the cylinder is â(100 + 64) = 12.8 cm
A 13 cm pencil of "0 diameter" would still not fit into the cylinder.
2006-12-03 06:24:07 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
10 Cm == s1, 8 Cm = s2.
Thus Lmax= (10^2+8^2)^(1/2)=12 Cm.
13>12 the pencil wont fit.
2006-12-03 07:50:39 · answer #3 · answered by mathman241 6 · 0⤊ 0⤋