WHOEVER ANSWERS FIRST GETS BRAINLY

The two rectangular prisms are similar. What is the volume of the larger rectangular prism? 240 cm³ 540 cm³ 1620 cm³ 3240 cm³ A

Andreas93 [3]

Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³

<h3>How to calculate volume of a rectangular prism?</h3>

If a rectangular prism has dimensions <u>a</u> unit, <u>b</u> unit, and <u>c</u> units, then its volume is given as

$V = a \times b \times c \: \rm unit^3$

<h3>What are similar figures?</h3>

They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.

For example,

if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then

the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and c x d units.

For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,

$60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12$

Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).

Thus, its dimensions would be 15, 3 x b, 3 x c

Thus, its volume would be

$15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3$

Thus,

The volume of the larger rectangular prism is given as: Option C: 1620 cm³

Learn more about volume of rectangular prism here:

brainly.com/question/21308574

5 0

2 years ago

Adiah played soccer for 1/2 hour she did homework for 5/4 hours

Komok [63]

That is not a question so I can't help you but combined she did 7/4 or 1 3/4 hours

8 0

3 years ago

the probability of winning a game is 20%. if you play 20 times how many times should you expect to win

julia-pushkina [17]

The probability of winning a game out of 20 is 4 times.

6 0

3 years ago

Read 2 more answers

You collect a total of $75 in donations from three people. The three donations are in the ratio 4 : 4 : 7. (hint: set up an equa

Amanda [17]

Answer:

Step-by-step explanation:

Since the ratio is 4x:4x:7x, if we add all those numbers up we get 15. Then we do 75/15 to get what x equals. So we get 5. So x equals 5. Following the rules of multiplication, you do 4(5):4(5):7(5), and simplifying that further, you get 20:20:35. If we add all those values up, we should get 75, and we do!

If you're wondering why I did 4x:4x:7x instead of 4:4:7, it's because a ratio is just a...well ratio? It's easier to visualize if you put a variable because the variable could be anything, and you would have to multiply all the given values to get the same proportions. In summery, I did it so it was easier to visualize

3 0

3 years ago

Hello! How do I find the surface area of this prism? Thanks!

Studentka2010 [4]

Answer: Choice C) 124 square cm

------------------------------------------------------------------

Explanation:

Let's calculate the area of the trapezoid shown
b1 and b2 are the parallel bases; h is the height of the 2D trapezoid
b1 = 2
b2 = 5
h = 1.5

A = h*(b1+b2)/2
A = 1.5*(2+5)/2
A = 1.5*7/2
A = 10.5/2
A = 5.25
The area of one 2D trapezoid is 5.25 sq cm
There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm
Keep this value (10.5) in mind. We'll use it later.

------------

Now onto the lateral surface area (LSA)
It turns out that the formula for the LSA is
LSA = p*d
where
p = perimeter of the trapezoid shown
d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier)
This formula works for any polygonal base. It doesn't have to be a trapezoid.

In this case the perimeter is,
p = 1.7+2+2.65+5
p = 11.35

So
LSA = p*d
LSA = 11.35*10
LSA = 113.5

Add this LSA to the base area found earlier
10.5+113.5 = 124

The total surface area is 124 square cm

8 0

3 years ago