Question

For the science fair a student prepared a model in the shape of a cylinder with radius 10 cm and height 40 cm closed at both the ends by cones with slant height 26 cm. How many litres of water can it contain? no spamming give me right ans only with full solution ​

Answer 1

Given,

For the science fair, a student prepared a model in the shape of a cylinder with a radius of 10 cm and height of 40 cm closed at both ends by cones with a slant height of 26 cm.

To find,

The amount of water that the model contains.

Solution,

The amount of water that the model contains is 17.6 litres.

To answer this question, we will follow the following steps:

As given in the question, we have,

The radius of cylinder = 10cm

The height of the cylinder or h = 40 cm

So,

The volume of a cylinder

$= \pi \: {r}^{2} \times h$

$= \pi \: {(10)}^{2} \times 40$

$= 4000\pi \: {cm}^{3} \: \: (i)$

Now,

The radius of a cone or 'r' = radius of cylinder = 10 cm

Slant height, 'l' of cone = 26 cm

Let 'h' be the height of the cone

So,

${h}^{2} = {l}^{2} - {r}^{2}$

$= {26}^{2} - {10}^{2}$

$= 676 - 100$

$= 576$

$h = \sqrt{576}$

$= 24 \: cm$

So,

The volume of two cones

$= 2 × \frac{1}{3} \pi \: {r}^{2} \times h$

$= \frac{2}{3} \times \pi \: \: {10}^{2} \times 24$

$= 1600\pi {cm}^{3} \: \: (ii)$

So, the volume of the model ( from 'i' and ''ii'')

$= 4000 + 1600 \pi {cm}^{3}$

$= 5600 \pi {cm}^{3}$

$= 17600 {cm}^{3}$

As one litre contains 1000 cubic centimetres of water.

So,

The volume of water in litres = 17.6 litres.

Henceforth, the amount of water contained by the model made by a student is 17.6 litres.

Answer 2

Answer:

The volume of the container is 13816 cm³

Step-by-step explanation:

We know that the capacity of the container = Volume of the cylinder + volume of the conical ends.

We know Volume of cylinder = πr²h

and Volume of cone = $\frac{1}{3}$ πr²h

and l² = r² + h²

where r is the radius

and h is the height

and l is the slant height

Therefore, for cone,

26² = 10² + h²

=> 676 = 100 + h²

=> 576 = h²

=> 24 = h

Therefore, Capacity = π * (10)² * 40 + 2 * $\frac{1}{3}$ * π * (10)² * 24

                                 = π * (10)² * 40 + 2 * $\frac{1}{3}$ * π* (10)² * 24

                                 = 4000π + 400π

                                 = 4400π

                                 = 4400 * 3.14

                                 = 13816 cm³

Therefore, the volume of the container is 13816 cm³