Question

A cabinet is the shape of a triangular prism. The triangular base has a base length of 14 inches and a base height of 22 inches. The cabinet is 67.5 inches tall. What is the volume of the cabinet?

Answer 1

As Per Provided Information

We have been asked to determine the volume of triangular Prism . Volume of Triangular Prism is calculated by using the following formula

`\bf \: Volume_((Triangular~Prism)) = \cfrac{1}{2} * b \: * h * l`

Substitute the given value and let's calculate the volume of cabinet .

`\sf \: \longrightarrow Volume_((Triangular~Prism)) \: = \cfrac{1}{2} * 14 * 22 * 67.5 \: \: \\ \\ \sf \: \longrightarrow Volume_((Triangular~Prism)) \: = (1)/( \cancel2) * \cancel14 * 22 * 67.5 \: \: \\ \\ \\ \sf \: \longrightarrow Volume_((Triangular~Prism)) \: = 7 * 22 * 67.5 \: \: \\ \\ \\ \sf \: \longrightarrow Volume_((Triangular~Prism)) \: = \: 154 * 67.5 \: \: \\ \\ \\ \sf \: \longrightarrow Volume_((Triangular~Prism)) \: = 10395 {cm}^(3)`

Therefore,

• Volume of the Triangular Prism Cabinet is 10395 cm³.