Question

A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches. Which expression shows the area of the base of each pyramid?
A. 1/3x^2 in.2
B. 1/4x^2 in.2
C. x2 in.2
D. 1/2x^2 in.2
Also...
A solid right pyramid has a square base with an edge length of x cm and a heigt of y cm. Which expression represents the volume of the pyramid?
A. 1/3x2y cm3
B. 1/2xy2 cm3
C. 1/3xy cm3
D. 1/2x2y cm3
This is all the info I am given HELP

Answer 1

Answer: A. (1/4 x)∧2 in.∧2

Just took quiz.

Answer 2

Answer:

Option B ⇒ Area of base of each pyramid :

$(\frac{x}{4})^2 in^2$

Option A ⇒ Volume of pyramid :

$\frac{1}{3} x^{2} \cdot y$   cm3

Step-by-step explanation:

One side of tile consists of 4 pyramids and since length of whole tile is x,

So, the base length of each pyramid = $\frac{x}{4}$

⇒ Area of base of each pyramid = side²

⇒ Area =

$(\frac{x}{4})^2 in^2$

Volume of square based pyramid :

$=(Area of base )\cdot \frac{h}{3}\\=\frac{x^2}{3} cm^3$

For 1. The correct Option is B

For 2. The correct option is A