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3 years ago

Find the volume of the rectangular prism. Express your answer as a simplified mixed number.

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

3 0

Answer:

414 9/16 m³

$414\frac{9}{16}m^{3}$

Step-by-step explanation:

The volume of a Rectangular prism is calculated as Length × Width × Height

From the attached diagram,we can see that

The length = 8 3/8 m

The width = 6 m

The height =8 1/4 m

Converting the mixed fraction to improper fraction in other to simplify it better

The length = 67/8 m

The height = 33/4 m

The volume of the rectangular prism =

67/8 m × 6m × 33/4m

= (13266/32)m³

= 6633/16 m³

= 414 9/16 m³

= $414\frac{9}{16}m^{3}$

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The perimeter of a triangle is 32 feet. One side of the triangle is 3 times the second side. The third side is 12 feet longer

Ivenika [448]

We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:

GiveN:

One side is 3 times the second side.
Third side is 12 feet longer than the second side.

As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.

So let the second side be x

Then,

First side = 3x
And, third side = x + 12

We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:

$3x + x + x + 12 = 32$

Solving it further,

$5x + 12 = 32$

Subtracting 12 from both sides,

$5x + 12 - 12 = 32 - 12$

$5x = 20$

Dividing 5 from both sides,

$\frac{5x}{5} = \frac{20}{5}$

$x = 4$

Then,

First side = 3x = 12 feet
Second side = 4 feet
Third side = x + 12 = 16 feet

And we are done with the answer !!

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3 years ago

The object on the right is made from a square-based pyramid joined to a cuboid.

spayn [35]

Answer:

Density of steel = 80.73 gm/ $cm^3$

Step-by-step explanation:

The figure is made up of cuboid and square pyramid.

Height of cuboid, h = 9 cm

Length of cuboid, l = 6 cm

Width of cuboid, w = 6 cm

Volume of cuboid is given by the formula:

$V_{Cuboid} = l \times w \times h$

$V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3$

Density of Wood , $D_{Cuboid}$ = 0.68g/ $cm^3$

We know that formula of Density is:

$Density = \dfrac{Weight}{Volume}$

$D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}$

Putting the values:

$W_{Cuboid} = 324 \times 0.68 = 220.32\ gm$

Total weight = $W_{Cuboid} + W_{Pyramid}$

970 = 220.32 $+ W_{Pyramid}$

$W_{Pyramid}$ = 749.68 gm

Volume of pyramid is given as:

$V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}$

Base is a square with side 6 cm

$V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3$

Density of Steel/Pyramid:

$D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3$

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4 years ago

Which property should Remus use to solve the equation below? 7 q = 49 division property of equality addition property of equalit

AysviL [449]

The division property of equality should Remus used to solve the given equation and this can be determined by using the given data.

Given :

Equation is $7q = 49$ .

The following steps can be used in order to determine the property that Remus use to solve the given equation:

Step 1 - Write the given equation.

$7q = 49$

Step 2 - The arithmetic operations can be used in order to evaluate the given equation.

Step 3 - Using the division property of equality the value of 'q' can be determined.

$q = \dfrac{49}{7}$

$q = 7$

Therefore, the correct option is A).

For more information, refer to the link given below:

brainly.com/question/11897796

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2 years ago

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A shade of green paint is made by mixing blue paint and yellow paint in the ratio of 4 to 3. How many pints of blue paint and ye

nexus9112 [7]

Answer:

$Blue = 12$

$Yellow = 9$

Step-by-step explanation:

Given

$Blue : Yellow = 4 : 3$

Required

Determine the number of pints of each to make 21 of green paints

First, calculate the total ratio.

$Total = 4 + 3$

$Total = 7$

The blue and the yellow pint can be represented individually as:

$Blue = \frac{4}{7} * Green$

$Yellow = \frac{3}{7} * Green$

Number of blue paint calculated last week is:

$Blue = \frac{4}{7} * 21$

$Blue = {4} * 3$

$Blue = 12$

$Yellow = \frac{3}{7} * Green$

$Yellow = \frac{3}{7} * 21$

$Yellow = {3} * 3$

$Yellow = 9$

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3 years ago

Figure PQRS is rotated counterclockwise

sleet_krkn [62]

I gotchu fam, a rotation is occurring and we know this because it’s rotating 180°. Figures PQRS and P’Q’R’S’ are congruent because they are the same shape and size, just in different places.

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3 years ago