Question

Prism J and prism K have the same volume. A cube J with height 10, length 4 and width 3 A right angled triangular prism K with breadth 10, height 3 and width w. What is the width w of prism K?

Answer 1

We have been given prism J and prism K have the same volume. A cube J with height 10, length 4 and width 3 A right angled triangular prism K with breadth 10, height 3 and width w. We are asked to find width w of the prism K.

We will use formulas of volume of cuboid and volume of triangular prism.

`\text{Volume of cuboid}=\text{Length}* \text{Width}* \text{Height}`

`\text{Volume of cuboid}=4* 3* 10`

`\text{Volume of cuboid}=120`

`\text{Volume of triangular prism}=(1)/(2)\text{Base length}* \text{Height}* \text{Width}`

`\text{Volume of triangular prism}=(1)/(2)* 10* 3* w`

`\text{Volume of triangular prism}=5* 3* w`

`\text{Volume of triangular prism}=15* w`

Now we will equate both volumes as we are told that prism J and prism K have the same volume.

`15* w=120`

`(15* w)/(15)=(120)/(15)`

`w=8`

Therefore, the width w of prism K is 8 units.