A storage bin has the shape of a Square Prism with a Pyramid top. What is the volume of the storage bin ifits side length is s = 3 in, the height of the prism portion is h = 11 in, and the overall height is H = 18 in?

A storage bin has the shape of a Square Prism with a Pyramid top What is the volume of the storage bin ifits side length is s 3 in the height of the prism porti class=

Respuesta :

Given,

The height of the shape is 18 inches.

The height of cuboidal part is 11 inches.

The height of pyramid part is 18- 11 = 7 inches.

The side of the cuboidal part is 3 inches.

The base of the pyramid part is also 3 inches.

The volume of the cuboidal part is,

[tex]\begin{gathered} \text{Volume =l}\times b\times h \\ \text{Volume =s}\times\text{s}\times h \\ \text{ =3}\times3\times11 \\ \text{ =}99inches^3^{} \end{gathered}[/tex]

The volume of pyramid part is,

[tex]\text{Volume =}a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex]

Here, the value of a is 3 and h is 7 then,

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