Answer:
16 times
Step-by-step explanation:
![\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)}](https://tex.z-dn.net/?f=%5Ctextsf%7BVolume%20of%20a%20cone%7D%3D%5Csf%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%20%5Cquad%5Ctextsf%7B%28where%20r%20is%20the%20radius%20and%20h%20is%20the%20height%29%7D)
If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.
![\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20Volume%20%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20%28ar%29%5E2h%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20%28a%5E2%29r%5E2h)
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 <u>16 times greater </u>than the smaller cone.
<h3><u>Proof</u></h3>
Given:
Substituting the given values into the formula:
![\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20Volume%20%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20%286%29%5E2%289%29%3D108%20%5Cpi%20%5C%3A%20%5C%3Acubic%5C%3Aunits)
If the radius is quadrupled:
- radius = 6 × 4 = 24
- height = 9
Substituting the new given values into the formula:
![\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20Volume%20%3D%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20%2824%29%5E2%289%29%3D1728%20%5Cpi%20%5C%3A%20%5C%3Acubic%5C%3Aunits)
To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:
![\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7BV_%7Blarge%7D%7D%7BV_%7Bsmall%7D%7D%3D%5Cdfrac%7B1728%5Cpi%7D%7B108%5Cpi%7D%3D16)
So the volume of the larger cone is <u>16 times greater</u> than the volume of the smaller cone.
Answer:
$252
Step-by-step explanation:
firstly we have to find how much tax cost.
to find tax turn the percentage into a decimal and multiply by the price of the item.
5% = 0.05
0.05 x $240 = $12
then once you have the tax add it to the price.
$240 + $12 = $252
and thats your answer!
hope this helps!
Answer:
The P-value for this test is P=0.00006.
Step-by-step explanation:
We have a matched-pair test, with a test statistic t=-14.9.
The degrees of freedom in a sample of 5 students is:
![df=n-1=5-1=4](https://tex.z-dn.net/?f=df%3Dn-1%3D5-1%3D4)
For a t=-14.9 and 4 degrees of freedom, a left-tail test will have a P-value of:
![P-value=P(t_4](https://tex.z-dn.net/?f=P-value%3DP%28t_4%3C-14.9%29%3D0.00006%5Capprox%200)
The claim is that the new unit on taking square roots is helping students to learn. This test concludes that there is statistical evidence to support the claim that the new unit is helping students to learn.
Answer:
108
Step-by-step explanation:
<u>find the volume of the cooler</u>:
V=πr²h
π×6²×16= 1809.56
<u>find the volume of the cup</u>:
V=πr²(h/3)
π×2²×(4/3)= 16.76
<u>divide the volume:</u>
1809.56/16.76= 107.969
Assuming that the cooler is full to the max, and cups are filled almost to the top, the cooler contains 108 cups of water.
Answer:
280 ml as a percentage of 140 l is 0.2%
Step-by-step explanation:
- Note that 1 liter = 1000 milliliters
- To find a percentage of a number divide the number by the total and multiply the quotient by 100%
∵ There is an amount of 280 ml
∵ The total amount is 140 l
→ Change the liter to milliliters using the 1st point above
∴ 140 l = 140 × 1000 = 140000 ml
∴ 140 l = 140,000 ml
→ Now divide the amount by the total, then multiply the quotient by 100%
∵ 280 ÷ 140,000 =
∵
× 100% = 0.2%
∴ 280 ml as a percentage of 140 l is 0.2%