Respuesta :
Answer:
Third option: 8 cm
Step-by-step explanation:
Volume of the pyramid: V=80 cm³
Base is a right triangle, and the adjacent sides of the right angle (the legs) measure 5 cm and 12 cm
Height of the pyramid: h=?
The formula to calculate the volume of a pyramid is:
[tex]V=\frac{A_{b}h}{3}[/tex]
Area of the base: Ab
The base is a right triangle, then to calculate its area we can use the formula to calculate the area of a right triangle:
[tex]A_{b}=\frac{Leg_{1}Leg_{2}}{2}\\ A_{b}=\frac{(5 cm)(12 cm)}{2}\\ A_{b}=\frac{60 cm^{2}}{2}\\ A_{b}=30 cm^{2}[/tex]
Replacing the known values in the formula of volume:
[tex]80 cm^{3}=\frac{(30 cm^{2})h}{3}\\ 80 cm^{3}=(10 cm^{2} )h[/tex]
Solving for h: Dividing both sides of the equation by 10 cm²:
[tex]\frac{80 cm^{3}}{10 cm^{2}}=\frac{(10 cm^{2})h}{10 cm^{2}}\\ 8 cm=h\\ h=8 cm[/tex]
