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vfiekz [6]
2 years ago
10

1. What is the volume for the following rectangular prism?

Mathematics
1 answer:
____ [38]2 years ago
8 0

Answer:

2. c) 1050 mm³

3. c) 8 yards.

Step-by-step explanation:

Given the following data;

Length = 25mm

Width = 7 mm

Height = 6 mm

To find the volume of the rectangular prism;

Volume of rectangular prism = base area * height

First of all, we would determine the base area;

Base area = length * width

Base area = 25 * 7

Base area = 175 mm²

Next, we find the volume;

Volume of rectangular prism = 175 * 6

Volume of rectangular prism = 1050 mm³

Question 2.

Given the following data;

Length = 9 yards

Width = 7.5 yards

Volume = 540 cubic yards

To find the height of the rectangular prism, x;

Volume of rectangular prism = length * width * height

540 = 9 * 7.5 * x

540 = 67.5x

x = 540/67.5

Height, x = 8 yards

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Part of the arena is being turned into a public darkroom. The floor needs covering in rubber tiles before work can begin on the
vladimir2022 [97]

The number of tiles used is 300 tiles.

According to the statement

We have given that:

The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.

And we have to find that the number of tiles used to prepare the dark room.

So, For this purpose we have to find the area of the room floor.

The area of the floor is 6 *3.

The area of the floor is 18 meter per square.

The area of the tile is 0.2*0.3

The area of the tile is 0.06 meter per square.

Now,

The number of tiles used is 18/0.06

The number of tiles used is 300.

So, The number of tiles used is 300 tiles.

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7 0
2 years ago
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq
stiv31 [10]

Answer:

18

Step-by-step explanation:

Remark

This is one of those questions that can throw you. The problem is that do you include the original rectangle or not. The way it is written it sounds like you shouldn't

However if you don't the question gives you 2 complex answers. (answers with the sqrt( - 1) in them.

Solution

Let the width = x

Let the length = x + 5

Area of the rectangle: L * w = x * (x + 5)

Area of the smaller squares (there are 2)

Area = 2*s^2

x = s

Area = 2 * x^2

Area of the larger squares = 2 * (x+5)^2

Total Area

x*(x + 5) + 2x^2 + 2(x + 5)^2 = 120                 Expand

x^2 + 5x + 2x^2 + 2(x^2 + 10x + 25) = 120     Remove the brackets

x^2 + 5x + 2x^2 + 2x^2 + 20x + 50 = 120      collect the like terms on the left

5x^2 + 25x +  50 = 120                                   Subtract 120 from both sides.

5x^2 + 25x - 70 = 0                                         Divide through by 5

x^2 + 5x - 14 = 0                                               Factor

(x + 7)(x - 2) = 0                                                 x + 7 has no meaning  

x - 2 =  0

x = 2                                                              

Perimeter

P = 2*w + 2*L

w = 2

L = 2 + 5

L = 7

P = 2*2 + 2 * 7

P = 4 + 14

P = 18

8 0
3 years ago
A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream. What is the rate of
nikitadnepr [17]
<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>

Given that,

A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream

Therefore,

Upstream distance = 165 km

Upstream time = 3 hours

<h3><u>Find upstream speed:</u></h3>

speed = \frac{distance}{time}\\\\speed = \frac{165}{3}\\\\speed = 55

Thus upstream speed is 55 km per hour

Downstream distance = 510 km

Downstream time = 6 hours

<h3><u>Find downstream speed:</u></h3>

speed = \frac{510}{6}\\\\speed = 85

Thus downstream speed is 85 km per hour

<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 85 ----- eqn 1

u - v = 55 ----- eqn 2

Solve both

Add them

u + v + u - v = 85 + 55

2u = 140

u = 70

<em><u>Substitute u = 70 in eqn 1</u></em>

70 + v = 85

v = 85 - 70

v = 15

Thus rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr

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