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MrRa [10]
4 years ago
6

A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 unit. How many 1/3 unit cubes d

oes it take to fill the prism
Mathematics
1 answer:
Ghella [55]4 years ago
5 0

Answer:

108 cubic units

Step-by-step explanation:

V  = 4 cubic units

v = (1/3)³ = 1/27 cubic units

V/v = 4/(1/27) = 4/1 x 27/1 = 108 cubic units

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3 years ago
The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0). Which conc
vodka [1.7K]

Answer:

They are similar by the definition of similarity in terms of a dilation.

Step-by-step explanation:

Given:

The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0).

To choose: the correct option

Solution:

According to distance formula distance between points (x_1,y_1),(x_2,y_2) is given by \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

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MN=\sqrt{(4-1)^2+(9-3)^2}=\sqrt{(3)^2+(6)^2}=\sqrt{45}\\NO=\sqrt{(7-4)^2+(3-9)^2}=\sqrt{(3)^2+(-6)^2}=\sqrt{45}\\\\MO=\sqrt{(7-1)^2+(3-3)^2}=\sqrt{(6)^2+(0)^2}=\sqrt{36}=6\\

For ΔPQR,

PQ=\sqrt{(4-3)^2+(2-0)^2}=\sqrt{(1)^2+(2)^2}=\sqrt{5}\\QR=\sqrt{(5-4)^2+(0-2)^2}=\sqrt{(1)^2+(-2)^2}=\sqrt{5}\\\\PR=\sqrt{(5-3)^2+(0-0)^2}=\sqrt{(2)^2+(0)^2}=2\\

So,

\frac{MN}{PQ}=\frac{\sqrt{45} }{\sqrt{5} }=\sqrt{9}=3\\ \frac{NO}{QR}=\frac{\sqrt{45} }{\sqrt{5} }=\sqrt{9}=3\\\frac{MO}{PR}=\frac{6 }{2 }=3\\

Therefore, They are similar by the definition of similarity in terms of a dilation.

Two triangles are said to be similar if their sides are proportional.

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