Respuesta :
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.
[tex]\text{Volume of cuboid}=\text{Length}\times \text{Width}\times \text{Height}[/tex]
[tex]\text{Volume of cuboid}=4\times 3\times 10[/tex]
[tex]\text{Volume of cuboid}=120[/tex]
[tex]\text{Volume of triangular prism}=\frac{1}{2}\text{Base length}\times \text{Height}\times \text{Width}[/tex]
[tex]\text{Volume of triangular prism}=\frac{1}{2}\times 10\times 3\times w[/tex]
[tex]\text{Volume of triangular prism}=5\times 3\times w[/tex]
[tex]\text{Volume of triangular prism}=15\times w[/tex]
Now we will equate both volumes as we are told that prism J and prism K have the same volume.
[tex]15\times w=120[/tex]
[tex]\frac{15\times w}{15}=\frac{120}{15}[/tex]
[tex]w=8[/tex]
Therefore, the width w of prism K is 8 units.
