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.

$\text{Volume of cuboid}=\text{Length}\times \text{Width}\times \text{Height}$

$\text{Volume of cuboid}=4\times 3\times 10$

$\text{Volume of cuboid}=120$

$\text{Volume of triangular prism}=\frac{1}{2}\text{Base length}\times \text{Height}\times \text{Width}$

$\text{Volume of triangular prism}=\frac{1}{2}\times 10\times 3\times w$

$\text{Volume of triangular prism}=5\times 3\times w$

$\text{Volume of triangular prism}=15\times w$

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

$15\times w=120$

$\frac{15\times w}{15}=\frac{120}{15}$

$w=8$

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