Mathematics, 04.02.2020 08:46 querty2400

The dimensions of a rectangular prism are shown below: length: 1 and 1 over 2feet width: 1 foot height: 2 and 1 over 2feet the lengths of the sides of a small cube are 1 over 2 foot each. part a: how many small cubes can be packed in the rectangular prism? show your work. (5 points) part b: use the answer obtained in part a to find the volume of the rectangular prism in terms of the small cube and a unit cube.

Answers: 3

Show answers

Answers

Answer from: MysteryDove12

A - 30 cubes

B - Volume of prism = $\frac{15}{4}$ feet³

Step-by-step explanation:

We are given that the dimensions of the rectangualr prism is,

Length = $1\frac{1}{2}$ = $\frac{3}{2}$ feet

Width = 1 foot

Height = $2\frac{1}{2}$ = $\frac{5}{2}$ feet

Thus, the volume of the prism = Length × Width × Height

i.e. Volume of the prism = $\frac{3}{2}$ × 1 × $\frac{5}{2}$ = $\frac{15}{4}$ feet³

Now, the side of the cube = $\frac{1}{2}$ foot each.

Volume of the cube = $(\frac{1}{2})^3$ = $\frac{1}{8}$ feet³

Part A: Number of cubes which can be packed inside the prism are given by,

Number of cubes = Volume of prism divided by Volume of cube

i.e. Number of cubes = $\frac{\frac{15}{4}}{\frac{1}{8}}$

i.e. Number of cubes = $\frac{15}{4} \times \frac{8}{1}$

i.e. Number of cubes = 15 × 2 = 30

Hence, 30 cubes can be packed inside the rectangular prism.

Part B: As we have, there are 30 cubes which can be fit inside the prism.

Since, the volume of 1 cube = $\frac{1}{8}$ feet³

So, Volume of 30 cube = $\frac{1}{8}\times 30$ = $\frac{15}{4}$ feet³

Thus, the volume of the rectangular prism is $\frac{15}{4}$ feet³.

Answer from: foreignev

Dimensions of a rectangular prism

Length

$=1\frac{1}{2}\\\\=\frac{3}{2}$ foot

Breadth

=1 foot

Height

$=2\frac{1}{2}\\\\=\frac{5}{2}$ foot

Volume of Rectangular prism

=Length × Breadth × Height

$=\frac{3}{2} \times 1 \times \frac{5}{2}\\\\=\frac{15}{4}\text{Cubic foot}$

Dimension of Cube is

Each side Length is $=\frac{1}{2}$ .

Volume of Cube is

=Side × Side ×Side

$=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\\\\=\frac{1}{8}\text{Cubic foot}$

Part A

Number of Small cubes which can be fitted inside a Rectangular Prism

$=\frac{\text{Volume of Rectangular prism}}{\text{Volume of cube}}\\\\=\frac{\frac{15}{4}}{\frac{1}{8}}\\\\=\frac{120}{4}\\\\=30$

Part B

⇒Volume of Rectangular prism=30 × Volume of cube having dimension $\frac{1}{2}$ .

→Volume of cube having side length 1 foot

=1×1×1

=1 cubic foot

⇒Volume of Rectangular prism= $\frac{15}{4}$ × Volume of cube having side of length 1 unit.

Answer from: Quest

On monday,mrs.wise bought 3 lbs of apples at $4per lb= 4*3=$12on tuesday ,20%off and she buy 5 lbs of apples = $4-20%=3.20*5lb=$16example: other wise when she buy 5lbs on monday she have to spend 4*5=20

Answer from: Quest

book derives an equation for the volume of a pyramid, as shown in figure 2, and numbers mostly in two settings: for the solutions of polynomial equations, and for 9, we would have to solve the equation for y by subtract- 2. the point (1,. 2) is the center of the circle whose equation is x2 y2. 2x. 4y p.w.c. davies.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Aregular hexagon rotates counterclockwise about its center. it turns through angles greater than 0° and less than or equal to 360°. at how many different angles will the hexagon map onto itself?

Answers: 2

Answer

Mathematics, 21.06.2019 18:10

Which point is a solution to y s 4x + 5?

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

Suppose your school costs for this term were $4900 and financial aid covered 3/4 of that amount. how much did financial aid cover? and how much do you still have to pay?

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Answers: 1

Answer

You know the right answer?

The dimensions of a rectangular prism are shown below: length: 1 and 1 over 2feet width: 1 foot h...

Questions