Question

A rectangular pyramid has a base with dimensions 5 inches by 7 inches. The height of the pyramid is unknown. If the volume of the pyramid is 105 cubic inches, what is the height of the pyramid? Explain the steps.

Answer 1

bearing in mind that the volume of a pyramid is the product of the area of its base and its height, now, this one has a rectangular base of 5x7, so its base area is 35.

$\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ ------\\ V=\stackrel{in^3}{105}\\ B=\stackrel{5\times 7}{35} \end{cases}\implies 105=\cfrac{1}{3}(35)h \\\\\\ 3(105)=35h\implies 315=35h\implies \cfrac{315}{35}=h\implies 9=h$

Answer 2

Answer:

Sample Response: Substitute the area of the base and the volume into the formula V = 1

3

Bh. After substituting, you have 105 = 1

3

(35)h. Solve for h by multiplying both sides by 3 and then dividing both sides by 35. The height is 9 inches.

Step-by-step explanation:

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