Question

Calculate the volume of the figure.

A. 15 cm^3
B. 33 cm^3
C.45 cm^3
D. 54 cm^3
Don't worry it's not a test question. It's a study guide question. I have a quiz in a few days and I need help thanks :)

Answer 1

Volume of square 3x3x3=27
Volume of a square pyramid 1/3 Bh. 1/3(9)2= 6
Total 33 cm^3. =. 27+6

Answer 2

B. 33 cm³

Explanation:

In the given figure,

A right square pyramid is placed on a face of cube so that their vertices coincide.

Since, the volume of the right square pyramid,

`V=a^2(h)/(3)`

Where, a is the base edge of the pyramid and h is the height of the pyramid,

Here, The height of pyramid, h= 2 cm,

The base edge of the pyramid, a = 3 cm,

Thus, the volume of the pyramid,

`V_1=(3)^2(2)/(3)=(18)/(3)=6\text{ cube cm}`

Now, the volume of a cube = ( side )³

Here, the side of the cube = 3 cm,

⇒ The volume of the cube,

`V_2 = (3)^3 = 27\text{ cube cm}`

Hence, the total volume of the figure = Volume of pyramid + Volume of the cube

`=V_1+V_2`

`=6+27`

`=33\text{ cube cm}`