Question

Find the volume of this square based pyramid.

12 cm

10cm
10cm


V=

Answer 1

Answer: 400 cm³

Step-by-step explanation:

Hey there! We must use the area of a square pyramid formula to solve this. The area is given by the area of the square base multiplied by the height of the pyramid.

Square Pyramid area formula: $\[\boxed{V = \frac{1}{3} \times \text{Base Area} \times \text{Height}}\]$

Solving:

We know that one of the base sides is 10, meaning the other is 10

$Base ~Area = 10~cm~\times 10~cm~ = 100~cm^2$

Now plug it into the formula and solve:

$\[V = \frac{1}{3} \times 100 \times 12 = \frac{1}{3} \times 1200 = \boxed{400 \, \text{cm}^3}\]$

There is your answer!

That's it

Answer 2

Answer:

$\sf V = 400 \textsf{ cm}^3$

Step-by-step explanation:

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

$\Large\boxed{\boxed{ \textsf{Volume} = \dfrac{1}{3} \times \textsf{base area} \times \textsf{height}}}$

Given:

• Base length = 10 cm
• Height = 12 cm

Find the Area of the Base:

Since the base of the pyramid is square, we can use the formula for the area of a square:

$\textsf{Area of base} = (\textsf{side length})^2$

$\textsf{Area of base} = (10 \textsf{ cm})^2$

$\textsf{Area of base} = 100 \textsf{ cm} ^2$

Calculate the Volume:

Now, use the formula for the volume of a pyramid:

$\textsf{Volume} = \dfrac{1}{3} \times \textsf{base area} \times \textsf{height}$

$\textsf{Volume} = \dfrac{1}{3} \times 100 \textsf{ cm}^2 \times 12 \textsf{ cm}$

$\textsf{Volume} = \dfrac{1}{3} \times 1200 \textsf{ cm}^3$

$\textsf{Volume} = 400 \textsf{ cm}^3$

Therefore, the volume of the square-based pyramid is:

$400 \textsf{ cm}^3$