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

Answer:

$\approx$ 11 litres 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, $h_1$ = 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.$\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2$

Here,

$r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm$

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:

$Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3$

Converting $cm^{3 }$ to litres:

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

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