jeyyy123
Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Question Help
Reasoning A cone with radius 6 and height 9 has its radius quadrupled. How many times greater is the
volume of the larger cone than the smaller cone?l

Sagot :

Let's see

For initial cone

  • r=6
  • h=9

Volume

  • 1/3πr²h
  • 1/3π(6)²(9)
  • 3(36)π
  • 108π units³

For new cone

  • r=4(6)=24
  • h=9

Volume

  • 1/3π(24)²(9)
  • 3(576)π
  • 1728π

So

  • 1728π/108π
  • 16times
semsee45

Answer:

16 times

Step-by-step explanation:

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.

[tex]\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h[/tex]

Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.

Proof

Given:

  • radius = 6
  • height = 9

Substituting the given values into the formula:

[tex]\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units[/tex]

If the radius is quadrupled:

  • radius = 6 × 4 = 24
  • height = 9

Substituting the new given values into the formula:

[tex]\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units[/tex]

To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:

[tex]\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16[/tex]

So the volume of the larger cone is 16 times greater than the volume of the smaller cone.

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.