Question

Hi Friends ,
Question :- A triangular plate of side 3cm, 4cm, 5cm is rotated about the longest side to form a double cone. Find the ratio of volume of cones???

Answer 1

Here we can see
3² + 4² = 5²
Hence given triangle is right triangle.

Cone1
Taking Height =4 cm
Slant height = Hypotenuse = 5
r = 3cm

Volume =
$\frac{1}{3}\pi \times 9 \times 4 \\ = 12\pi$
Cone2
Taking Height as 3
Radius as 4
slant height would be hypotenuse that is 5

Volume =
$\frac{1}{3} \pi \times 16 \times 3 \\ = 16\pi$
Ratio = 12π:16π
=
$\frac{12\pi}{16\pi} \\ = \frac{3}{4}$
Hence ratio is 3:4


Hope I am correct brother

Answer 2

Answer:

answer is 9:16

step by step explanation

3^2+4^2=5^2

9+16=25

let volumes be v and v'

let h=16 cm

radius=9cm

v=1/3×22/7×9cm^2×16cm

1/3×22/7×81cm×16cm

=9504/7cm

let h=9cm

radius=16cm

v'=1/3×22/7×16cm^2×9cm

1/3×22/7×256cm×9cm

=16896/7

v/v'=16896/7×7/9504

v:v'=16:9

v':v=9:16

hope it's correct