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The respective ratio of radii of two right circular cylinders (A and B) is 3 : 2. The respective ratio of volumes of cylinders A and B is 9 : 7, then what are the heights of cylinders A and B ?
- A8 : 5
- B4 : 7
- C7 : 6
- D5 : 4
Answer not set
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0
CCommunity
Solution
Volume of a cylinder = $\pi r^2 h$
where r and h are radius and height of the cylinder respectively.
Let $r_1$ , $h_1$ , $r_2$ and $h_2$ be the radius and heights of the two cylinders respectively.
$\pi (r_1)^2 h_1$ : $\pi (r_2)^2 h_2$ = 9 : 7 ------------- 1
Ratio of radii $r_1 : r_2 = 3 : 2$
Ratio of square of radii = 9 : 4
Replacing the ratio of radii in 1
$9h_1 : 4h_2$ $= 9: 7$
$h_1 : h_2$ $= (9\times 4) : (7\times 9)= 4 : 7$
Option B is the correct answer.
Volume of a cylinder = $\pi r^2 h$
where r and h are radius and height of the cylinder respectively.
Let $r_1$ , $h_1$ , $r_2$ and $h_2$ be the radius and heights of the two cylinders respectively.
$\pi (r_1)^2 h_1$ : $\pi (r_2)^2 h_2$ = 9 : 7 ------------- 1
Ratio of radii $r_1 : r_2 = 3 : 2$
Ratio of square of radii = 9 : 4
Replacing the ratio of radii in 1
$9h_1 : 4h_2$ $= 9: 7$
$h_1 : h_2$ $= (9\times 4) : (7\times 9)= 4 : 7$
Option B is the correct answer.
0
CCommunity
Solution
Volume of a cylinder = $\pi r^2 h$
where r and h are radius and height of the cylinder respectively.
Let $r_1$ , $h_1$ , $r_2$ and $h_2$ be the radius and heights of the two cylinders respectively.
$\pi (r_1)^2 h_1$ : $\pi (r_2)^2 h_2$ = 9 : 7 ------------- 1
Ratio of radii $r_1 : r_2 = 3 : 2$
Ratio of square of radii = 9 : 4
Replacing the ratio of radii in 1
$9h_1 : 4h_2$ $= 9: 7$
$h_1 : h_2$ $= (9\times 4) : (7\times 9)= 4 : 7$
Option B is the correct answer.
Volume of a cylinder = $\pi r^2 h$
where r and h are radius and height of the cylinder respectively.
Let $r_1$ , $h_1$ , $r_2$ and $h_2$ be the radius and heights of the two cylinders respectively.
$\pi (r_1)^2 h_1$ : $\pi (r_2)^2 h_2$ = 9 : 7 ------------- 1
Ratio of radii $r_1 : r_2 = 3 : 2$
Ratio of square of radii = 9 : 4
Replacing the ratio of radii in 1
$9h_1 : 4h_2$ $= 9: 7$
$h_1 : h_2$ $= (9\times 4) : (7\times 9)= 4 : 7$
Option B is the correct answer.