Question

Brooklyn bought a snowcone from the local shop. It is shaped like a cone topped with a half-sphere.

The cone has a height of 6 in. and a radius of 2 in.
What is the approximate volume of the whole shape? Round your answer to the nearest tenth.
Use 3.14 to approximate pi. (Show your work.)

Answer 1

The approximate volume of the whole shape is 41.9 in

Explanation:

Provided:

height = 6

radius = 2

The total volume:

Variables:

`Vt = total\;volume`

`Vcone = volume\:of\:a\:cone=( 1 )/( 3 ) \pi { r }^( 2 ) h`

`Vhemisphere = volume\:of\:a\:hemisphere= ( 2 )/( 3 ) \pi { r }^( 3 )`

`Vt = Vcone + Vhemisphere`

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

`Vt = ( 1 )/( 3 ) \left( 3.14 \right) { \left( 2 \right) }^( 2 ) \left( 6 \right) + ( 2 )/( 3 ) \left( 3.14 \right) { \left( 2 \right) }^( 3 )`

`\mathrm{Remove\:all\:parenthesis}`

`Vt = ( 1 )/( 3 )* \left 3.14 \right* { \left 2 \right }^( 2 )* \left 6 \right + ( 2 )/( 3 ) *\left 3.14 \right* { \left 2 \right }^( 3 )`

`\mathrm{Do\:the\:exponents\:first}`

`Vt = ( 1 )/( 3 )* \left 3.14 \right* 4* \left 6 \right + ( 2 )/( 3 ) *\left 3.14 \right* 8`

`\mathrm{Multiply\:( 1 )/( 3 )\:and\:3.14}`

`Vt = 1.04666667 \right* 4* \left 6 \right + ( 2 )/( 3 ) *\left 3.14 \right* 8`

`\mathrm{Multiply\:( 2 )/( 3 )\:and\:3.14}`

`Vt = 1.04666667 \right* 4* \left 6 \right + 2.09333333* 8`

`\mathrm{Multiply\:1.04666667\:by\:4\:and\:then\:by\:6}`

`Vt = 25.12 + 2.09333333* 8`

`\mathrm{Multiply\:2.09333333\:by\:8}`

`Vt = 25.12 + 16.746667`

`\mathrm{Add\:25.12\:and\:16.746667}`

`Vt = 41.866667`

`\mathrm{41.866667\:rounded\:to\:the\:nearest\:tenth\:is\:41.9}`

`Vt = 41.9`