find the volume of a pyramid with a square base, where the area of the base is 19.6 cm² and the height of…

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: Substitute the given values into the formula

We are given that ( B = 19.6\space cm^{2} ) and ( h=12.7\space cm ). Substituting these values into the formula, we get ( V=\frac{1}{3}\times19.6\times12.7 ).

Step3: Calculate the value

First, calculate ( 19.6\times12.7 = 248.92 ). Then, divide this result by 3: ( V=\frac{248.92}{3}\approx82.9733\space cm^{3} ).

Step4: Round to the nearest tenth

Rounding ( 82.9733 ) to the nearest tenth gives ( 83.0 ) (since the hundredth digit is 7, which is greater than or equal to 5, we round up the tenth digit).

Answer:

( 83.0\space cm^{3} )