Answer:
The capacity of the container is 2546.78 cm³.
Step-by-step explanation:
The volume of the frustum of a cone is:
![\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}]](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%3D%5Cfrac%7B%5Cpi%20h%7D%7B3%7D%5Ccdot%5BR%5E%7B2%7D%2BRr%2Br%5E%7B2%7D%5D)
The information provided is:
r = 16/2 = 8 cm
R = 24/2 = 12 cm
h = 8 cm
Compute the capacity of the container as follows:
![\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}]](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%3D%5Cfrac%7B%5Cpi%20h%7D%7B3%7D%5Ccdot%5BR%5E%7B2%7D%2BRr%2Br%5E%7B2%7D%5D)
![=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cpi%5Ccdot8%7D%7B3%7D%5Ccdot%5B%2812%29%5E%7B2%7D%2B%2812%5Ccdot%208%29%2B%288%29%5E%7B2%7D%5D%5C%5C%5C%5C%3D%5Cfrac%7B8%5Cpi%7D%7B3%7D%5Ctimes%20%5B144%2B96%2B64%5D%5C%5C%5C%5C%3D%5Cfrac%7B8%5Cpi%7D%7B3%7D%5Ctimes304%5C%5C%5C%5C%3D2546.784445%5C%5C%5C%5C%5Capprox%202546.78)
Thus, the capacity of the container is 2546.78 cm³.
Answer:
exact volume= 12320ft³
approximate volume= 12308.8ft³
Step-by-step explanation:
exact volume= 22/7×14² x 20
approximate volume = 3.14x14²x20
It will take her 4 days to read 1/3 of the book.
The answer is 4.
Answer:
See below ~
Step-by-step explanation:
<u>Given</u>
- Maitri and Aabhas do a work in 12 hours
- Aabhas and Kavya do the work in 15 hours
- Kavya and Maitri do the work in 20 hours
<u>Solving</u>
- Take Maitri, Aabhas, and Kavya to be x, y, z respectively
- <u>x + y = 12</u> (1)
- <u>y + z = 15</u> (2)
- <u>x + z = 20</u> (3)
<u>Take Equation 1 and rewrite it so that it is equal to x.</u>
<u>Take Equation 2 and rewrite it so that it is equal to z.</u>
<u>Now, substitute these values in Equation 3.</u>
- x + z = 20
- 12 - y + 15 - y = 20
- -2y + 27 = 20
- 2y = 7
- y = 7/2 = <u>3.5 hours [Aabhas]</u>
<u></u>
<u>Substitute the value of y in Equation 1.</u>
- x + 3.5 = 12
- x = <u>8.5 hours [Maitri]</u>
<u>Substitute the value of y in Equation 2.</u>
- 3.5 + z = 15
- z = <u>11.5 hours [Kavya]</u>
<u></u>
<u>Add the values of x, y, and z together.</u>
- x + y + z
- 8.5 + 3.5 + 11.5
- 12 + 11.5
- <u>23.5 hours [together]</u>