Question

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triangular based prism has a volume of 562 cm² and a base area of 63 cm². the height of the prism (correct to the nearest cm) is? h = vertical height a = base area

Explanation:

Step1: Recall the volume formula for a prism

The volume \( V \) of a prism is given by the formula \( V = A \times h \), where \( A \) is the base area and \( h \) is the height of the prism.

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

We can rearrange the formula to \( h=\frac{V}{A} \).

Step3: Substitute the given values

We know that \( V = 562\space cm^3 \) and \( A = 63\space cm^2 \). Substituting these values into the formula, we get \( h=\frac{562}{63} \).

Step4: Calculate the value of \( h \)

Calculating \( \frac{562}{63}\approx8.92 \). Rounding to the nearest cm, we get \( h\approx9 \).

Answer:

The height of the prism is \( \boldsymbol{9}\space cm \).