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 :)

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lisee7 lisee7 · Answer 1 · 2017-05-10T09:48:55+02:00

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

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-04-13T07:02:23+02:00

Answer:

B. 33 cm³

Step-by-step 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,

[tex]V=a^2\frac{h}{3}[/tex]

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,

[tex]V_1=(3)^2\frac{2}{3}=\frac{18}{3}=6\text{ cube cm}[/tex]

Now, the volume of a cube = ( side )³

Here, the side of the cube = 3 cm,

⇒ The volume of the cube,

[tex]V_2 = (3)^3 = 27\text{ cube cm}[/tex]

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

[tex]=V_1+V_2[/tex]

[tex]=6+27[/tex]

[tex]=33\text{ cube cm}[/tex]