Question

Determine how many litres of water will fit inside the following container. Round answer and all calculations to the nearest whole number.

Answer 1

`\approx` 11 litres of water will fit inside the container.

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,
`h_1` = 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+(1)/(3)\pi r_2^2 h_2`

Here,

`r_1=r_2 = (Diameter)/(2) = (26)/(2) =13\ cm`

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`

Now, putting the values to find the volume of container:

`Volume_(Container) = \pi * 13^2 * 15+(1)/(3)\pi * 13^2 * 15\\\Rightarrow Volume_(Container) = \pi * 13^2 * 15+\pi * 13^2 * 5\\\Rightarrow Volume_(Container) = \pi * 13^2 * 20\\\Rightarrow Volume_(Container) = 10613.2 \approx 10613\ cm^3`

Converting
`cm^(3 )` to litres:

`10613 cm^3 = 10.613\ litres \approx 11\ litres`

`\approx` 11 litres of water will fit inside the container.