Question

find the volume of a pyramid with a height of 29 cm and a rectangular base with dimensions of 3 cm and 10 cm. round your answer to the nearest hundredth as needed.

cm³

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Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step2: Calculate the area of the rectangular base

The base is a rectangle with length \( l = 10\space\text{cm} \) and width \( w=3\space\text{cm} \). The area of a rectangle is \( B=l\times w \), so \( B = 10\times3=30\space\text{cm}^2 \).

Step3: Substitute the values into the volume formula

We know \( B = 30\space\text{cm}^2 \) and \( h = 29\space\text{cm} \). Substituting into \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}\times30\times29 \).
First, calculate \( \frac{1}{3}\times30 = 10 \). Then, \( 10\times29=290 \).

Answer:

\( 290.00 \)