Question

Help me please!!!!!!​

Answer 1

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

Given :-

• A box of clay contains 25 packs

Each pack is a cuboid having dimensions 10cm × 10cm × 4 cm

To Find :-

• We have to find the no of spheres of radius 6cm can Jack make from a box of clay .

Let's Begin :-

Here, we have

• Length of one pack = 10cm
• Breath of 1 pack = 10 cm
• Height of 1 pack = 4 cm

We know that,

Volume of cuboid

`\bold{\red{ = length }}{\bold{\red{*{ breath }}}}{\bold{\red{*{height}}}}`

Subsitute the required values,

`\sf{ = 10 }{\sf{*{ 10}}}{\sf{*{4 }}}`

`\sf{ = 100 }{\sf{*{ 4}}}`

`\bold{ = 400\: cm² }`

Thus, The volume of 1 pack is 400 cm²

Now,

We know that,

Volume of sphere

`\bold{\pink{ = }}{\bold{\pink{(4)/(3)}}}{\bold{\pink{\pi{r^(3)}}}}`

Subsitute the required values,

`\sf{ = }{\sf{(4)/(3)}}{\sf{*{ 3.14 }}}{\sf{*{(6)^(3)}}}`

`\sf{ = }{\sf{(4)/(3)}}{\sf{*{ 3.14 }}}{\sf{*{216}}}`

`\sf{ = 4}{\sf{*{ 3.14 }}}{\sf{*{72}}}`

`\sf{ = 288}{\sf{*{ 3.14 }}}`

`\bold{ = 91.71 cm^(3)}`

Therefore,

No of spheres formed by 1 packs of cuboid

n = Volume of 1 packs/ Volume of sphere

Subsitute the required values,

`\sf{ n = }{\sf{( 400)/(91.71)}}`

`\bold{ n = 4.36 }`

Thus, The number of spheres formed by 1 pack of cuboid are 4.36

Therefore,

Total number of spheres formed by 25 packs

`\sf{ = 25 }{\sf{*{ 4.36}}}`

`\bold{ = 109 }`

Hence, The total number of spheres made by Jack from a box of clay is 109 spheres.