Respuesta :

semsee45

Answer:

300 yd³

Step-by-step explanation:

To find the volume of the given figure we can use the formula for the volume of a square-based pyramid:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Square-based Pyramid}}\\\\V =\dfrac{1}{3}b^2h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$b$ is the length of the base edge.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height perpendicular to the base.}\end{array}}[/tex]

In this case:

  • b = 10 yd
  • h = 9 yd

Substitute the values into the formula and solve for V:

[tex]V =\dfrac{1}{3}\cdot 10^2\cdot 9\\\\\\V =\dfrac{1}{3}\cdot 100\cdot 9\\\\\\V=\dfrac{1}{3} \cdot 900\\\\\\V =\dfrac{900}{3}\\\\\\V=300\; \sf yd^3[/tex]

Therefore, the volume of the given figure is 300 yd³.

msm555

Answer:

300 yd³

Step-by-step explanation:

To find the volume of a square-based pyramid, we can use the formula:

[tex]\large\boxed{\boxed{ \sf Volume(V)= \dfrac{1}{3} \times a^2 \times h }}[/tex]

Where:

  • [tex]\bold{ a }[/tex] is the length of one side of the base (in this case, [tex]\bold{ a = 10 }[/tex] yards)
  • [tex]\bold{ h }[/tex] is the height of the pyramid (in this case, [tex]\bold{ h = 9 }[/tex] yards)

Now, let's substitute the values into the formula and calculate:

[tex]\begin{aligned} \sf Volume(V) & = \dfrac{1}{3} \times 10^2 \times 9 \\\\ & = \dfrac{1}{3} \times 100 \times 9 \\\\ & = \dfrac{900}{3}\\\\ & = 300 \end{aligned} [/tex]

So, the volume of the square-based pyramid is 300 yd³.

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