Question

If the ratio of radii of two cones are 1:2. And the ratio of height is 3:4. Find the ratio of volume

Answer 1

Answer:

given

radii 1:2

hight 3:4

to find ratio of volume

formula = {1/3(πr^2)h}

{1/3(πx1)x(3)^2 } / {1/3(πx4)x16}

after cancelling the same value in denominator and numerator

we get

9/64

hence ratio of volume

are

9:64

Answer 2

Given,

• The ratio of radii of two cones is 1 : 2.
• The ratio of height is 3 : 4.

To Find,

• The Ratio Of Volume .

Solution,

Let's,

The Radius Of First Cone = X

So,

The Radius Of Second Cone = 2X

Let's,

The Height Of First Cone = 3Y

So,

The Height Of Second Cone = 4Y

Volume of First Cone

$: \implies \frac{1}{3} \pi {r}^{2} h \\ \\ : \implies \frac{\pi}{3} \times {x}^{2} \times 3y \\ \\ : \implies \pi {x}^{2} y$

Volume of Second Cone

$: \implies \frac{1}{3} \pi {r}^{2} h \\ \\ : \implies \frac{\pi}{3} {(2x)}^{2} (4y) \\ \\ : \implies \frac{\pi}{3} \times {4x}^{2} \times 4y \\ \\ : \implies \frac{16\pi {x}^{2}y }{3}$

Required Answer,

$: \implies \frac{\pi {x}^{2} y}{ \frac{16}{3}\pi {x}^{2} y } \\ \\ : \implies \frac{1}{ \frac{16}{3} } = 1 \div \frac{16}{3} = 1 \times \frac{3}{16} \\ \\ : \implies 3 \: : 16$

The Ratio Of Their Volumes