Question
- The figure shows a cube
of side
and
.
(a) Find the volume of the pyramid
.
(b) Find the total surface area of the pyramid
.
(a) Find the volume of the pyramid
(b) Find the total surface area of the pyramid
Ask by Watson Pearson. in Hong Kong
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) 金字塔的體積為約170.67立方厘米。
(b) 金字塔的總表面積為
平方厘米。
Solution

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The Deep Dive
To solve the problem, let’s start with the calculations step-by-step.
(a) To find the volume of the pyramid
, we can use the formula for the volume of a pyramid, which is:
The base of the pyramid is the square
. Since it’s a cube with side length
cm, the area of the base
is:
The height of the pyramid
from the base
is equal to the side of the cube, which is
cm.
Now, substitute these values into the volume formula:
(b) To find the total surface area of the pyramid
, we need to calculate the area of the base and the areas of the triangular faces.
The area of the base
is
.
Now, we will find the area of the triangular faces
. Each triangular face has a base of
and a height (the slant height from
to the base) that we will calculate. The height from
to the midpoint of any side of the square base is given by the Pythagorean theorem.
The distance from
to any vertex of the base (like
) is:
Each triangle has a height from
to the base
of:
The area of each triangle is
, so for one triangle:
To find
:
The area of one triangular face is:
Now, since there are four triangular faces:
Finally, the total surface area of the pyramid is:
So, the final answers are approximately:
(a) or
,
(b) or
.
(a)
(b)