Question

a solid iron toy consisting of a right circular cone of lateral height 5cm and the base diameter is 8cm is surmounted by hemisphere is placed upright in a right circular cylinder full of water such that it touches the bottom find the volume of the water left in the cylinder if the radius of the cylinder is 4cm and height is 5cm​

Answer 1

Answer:

The Volume of water left in cylinder is 33.49 cm³ .

Step-by-step explanation:

Given as :

Let The volume of water left in cylinder = x cubic centimeter

The height of cylinder = 5 cm

The radius of cylinder = 4 cm

So, The volume of cylinder = π × radius² × height

Or, The volume of cylinder = 3.14 × 4² × 5

Or, The volume of cylinder = 251.2 cm³

Again

The height of cone = 5 cm

The diameter of cone = 8 cm

So, The radius of cone = $\dfrac{diameter}{2}$ = 4 cm

So, The volume of cone = $\dfrac{1}{3}$ × π × radius² × height

Or, The volume of cone = $\dfrac{1}{3}$ × 3.14 × 4² × 5

Or, The volume of cone = 83.73  cm³

Again

The radius of hemisphere = radius of cone = 4 cm

So, volume of hemisphere = $\dfrac{2}{3}$ × π × radius³

Or, volume of hemisphere = $\dfrac{2}{3}$ × 3.14 × 4³

Or, volume of hemisphere = 133.973 cm³

Volume of water left in cylinder = volume of cylinder - ( volume of cone + volume of hemisphere )

Or,  x = 251.2 cm³ - (  83.73  cm³ + 133.973 cm³ )

Or, x = 251.2 cm³ - 217.703 cm³

∴ x = 33.49 cm³

So, Volume of water left in cylinder = x  = 33.49 cm³

Hence, The Volume of water left in cylinder is 33.49 cm³ . Answer

Answer 2

Step-by-step explanation:

The volume of water left in cylinder = x cubic centimeter

The height of cylinder = 5 cm

The radius of cylinder = 4 cm

So, The volume of cylinder = π × radius² × height

Or, The volume of cylinder = 3.14 × 4² × 5

Or, The volume of cylinder = 251.2 cm³

Again

The height of cone = 5 cm

The diameter of cone = 8 cm

So, The radius of cone = \dfrac{diameter}{2}

2

diameter

= 4 cm

So, The volume of cone = \dfrac{1}{3}

3

1

× π × radius² × height

Or, The volume of cone = \dfrac{1}{3}

3

1

× 3.14 × 4² × 5

Or, The volume of cone = 83.73 cm³

Again

The radius of hemisphere = radius of cone = 4 cm

So, volume of hemisphere = \dfrac{2}{3}

3

2

× π × radius³

Or, volume of hemisphere = \dfrac{2}{3}

3

2

× 3.14 × 4³

Or, volume of hemisphere = 133.973 cm³

Volume of water left in cylinder = volume of cylinder - ( volume of cone + volume of hemisphere )

Or, x = 251.2 cm³ - ( 83.73 cm³ + 133.973 cm³ )

Or, x = 251.2 cm³ - 217.703 cm³

∴ x = 33.49 cm³

So, Volume of water left in cylinder = x = 33.49 cm³

Hence, The Volume of water left in cylinder is 33.49 cm³ . Answer