Answer:
The volume of this pyramid is 16 cm³.
Step-by-step explanation:
The volume
of a solid pyramid can be given as:
,
where
is the area of the base of the pyramid, and
is the height of the pyramid.
Here's how to solve this problem with calculus without using the previous formula.
Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.
Refer to the sketch attached. Let the vertical distance from the vertice be
cm.
- At the vertice of this pyramid,
and the length of a side of the square is also
. - At the base of this pyramid,
and the length of a side of the square is
cm.
As a result, the length of a side of the square will be
.
The area of the square will be
.
Integrate the area of the horizontal cross-section with respect to
- from the top of the pyramid, where
, - to the base, where
.
.
In other words, the volume of this pyramid is 16 cubic centimeters.
Yes because all equilateral triangles have equal angles and side lengths so they are all similar. hope i helped -J
Answer:the answeer is
= 72 ft³
Step-by-step explanation:
Multiply the width of the wall by its height. So one of the walls is 80 square feet (10 feet wide x 8 feet high) and the other is 96 square feet (12 feet x 8 feet). If you need the total square footage of the walls - for figuring paint or wallpaper for example - you can simplify the calculation by first adding all the wall lengths together, then multiplying by the height (10 + 12 + 10 + 12 = 44 x 8 = 352 square feet of total wall area).
The answer is both triangles A and D
Hope this helps :)