Answer:
<em>11 litres </em>of water will fit inside the container.
Step-by-step explanation:
As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.
Given:
Height of cylinder,
= 15 cm
Diameter of cylinder/ cone, D = 26 cm
Slant height of cone, l = 20 cm
Here, we need to find the volume of container.![\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2](https://tex.z-dn.net/?f=%5C%5CVolume_%7BContainer%7D%20%3D%20Volume_%7BCylinder%7D%2BVolume_%7BCone%7D%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%20%5Cpi%20r_1%5E2%20h_1%2B%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r_2%5E2%20h_2)
Here,
![r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm](https://tex.z-dn.net/?f=r_1%3Dr_2%20%3D%20%5Cdfrac%7BDiameter%7D%7B2%7D%20%3D%20%5Cdfrac%7B26%7D%7B2%7D%20%3D13%5C%20cm)
To find the Height of Cylinder, we can use the following formula:
![l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm](https://tex.z-dn.net/?f=l%5E2%20%3D%20r_2%5E2%2Bh_2%5E2%5C%5C%5CRightarrow%20h_2%5E2%20%3D%2020%5E2-13%5E2%5C%5C%5CRightarrow%20h_2%5E2%20%3D%20400-169%5C%5C%5CRightarrow%20h_2%5E2%20%3D%20231%5C%5C%5CRightarrow%20h_2%3D15.2%5C%20cm%20%5Capprox%2015%5C%20cm)
Now, putting the values to find the volume of container:
![Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3](https://tex.z-dn.net/?f=Volume_%7BContainer%7D%20%3D%20%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2015%2B%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2015%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%20%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2015%2B%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%205%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%20%5Cpi%20%5Ctimes%2013%5E2%20%5Ctimes%2020%5C%5C%5CRightarrow%20Volume_%7BContainer%7D%20%3D%2010613.2%20%5Capprox%2010613%5C%20cm%5E3)
Converting
to litres:
![10613 cm^3 = 10.613\ litres \approx 11\ litres](https://tex.z-dn.net/?f=10613%20cm%5E3%20%3D%2010.613%5C%20litres%20%5Capprox%2011%5C%20litres)
<em>11 litres </em>of water will fit inside the container.