Question

a tetrahedron has a vertical height of 9.1 cm and a volume of 103 cm³. find the base area of the tetrahedron (correct to the nearest 10th of a cm²).

Explanation:

Step1: Recall the volume formula for a tetrahedron

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

Step2: Rearrange the formula to solve for \( A \)

Starting with \( V = \frac{1}{3}Ah \), we can multiply both sides by 3 to get \( 3V=Ah \). Then, divide both sides by \( h \) to solve for \( A \), so \( A=\frac{3V}{h} \).

Step3: Substitute the given values

We know that \( V = 103\space cm^3 \) and \( h = 9.1\space cm \). Substituting these values into the formula for \( A \), we get \( A=\frac{3\times103}{9.1} \).

Step4: Calculate the value

First, calculate the numerator: \( 3\times103 = 309 \). Then, divide by 9.1: \( A=\frac{309}{9.1}\approx33.956\space cm^2 \). Rounding to the nearest tenth, we get \( A\approx34.0\space cm^2 \).

Answer:

The base area of the tetrahedron is approximately \( 34.0\space cm^2 \).