Question

Roslyn is an engineer. She is designing a part for a new engine. The length of the part is 16 centimeters (cm), the width is 6 cm, and the height of the cone top is 5 cm, as shown.

Answer 1

`\bold{\huge{\underline{ Solution }}}`

Given :-

• The length of the part is 16 centimeters
• The part of new engine is composed of 1 cone, 1 cylinder and 1 hemisphere
• The width of the engine is 6 cm
• The height of the cone is 5 cm

To Find :-

• We have to find the total volume of the part

Let's Begin :-

Let divide the part of engine into three parts as it is composed of 3 different figures.

We know that,

Volume of cone

`\bold{=}{\bold{( 1)/(3)}}{\bold{{\pi}r^(2)h}}`

Here, we have,

• The height of the cone is 5 cm
• The diameter of the cone is 6 cm
• Therefore,
• Radius of the cone = 3 cm

Subsitute the required values,

Volume of the first part that is cone

`\sf{=}{\sf{( 1)/(3)}}{\sf{ {*}3.14{*}(3)^(2){*}5}}`

`\sf{=}{\sf{( 1)/(3)}}{\sf{ {*}3.14{*}9{*}5}}`

`\sf{ = 3.14 {*} 3 {*} 5 }`

`\sf{ = 3.14 {*} 15 }`

`\sf{ = 3.14 {*} 15 }`

`\bold{ = 47.1 cm^(3) }`

Thus, The volume of cone is 47.1 cm³ .

For second part

• Second part is composed of cylinder

We know that,

The volume of cylinder

`\bold{ = {\pi}r^(2)h }`

Here,

• The diameter of the cylinder is 6 cm
• So, Radius = 3 cm
• The length of the cylinder = 16 - (Length of cone + Length of hemisphere)
• Length = 16 - 11 = 5 cm

Subsitute the required values in the above formula,

Volume of the second part that is cylinder

`\sf{ = 3.14{*} (3)^(2){*} 5}`

`\sf{ = 3.14{*} 9 {*} 5}`

`\sf{ = 3.14{*} 45 }`

`\bold{ = 141.3 cm^(3)}`

Thus, The volume of the cylinder is 141.3 cm³

For third part

• Third part is composed of hemisphere

We know that,

Volume of hemisphere

`\bold{=}{\bold{( 2)/(3)}}{\sf{ {\pi}r}}`

Here,

• The diameter of the hemisphere is 6 cm
• So, Radius = 3cm

Subsitute the required values,

Volume of third part that is hemisphere

`\sf{=}{\sf{( 2)/(3)}}{\sf{{*} 3.14 {*}3}}`

`\sf{ = 2 {*} 3.14 }`

`\bold{ = 6.28 cm^(3) }`

Thus, The volume of the hemisphere is 6.28 cm³

Therefore,

The total volume of the part

= Volume of cone + Volume of cylinder + Volume of hemisphere

`\sf{ = 47.1 + 141.3 + 6.28 }`

`\sf{ = 188.4 + 6.28 }`

`\sf{ = 194.68 cm^(3) }`

`\bold{ = 194.7 cm^(3) }`

Hence, The total volume of the part is 194.7 cm³ .