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SVEN [57.7K]
2 years ago
15

Consider the shape below. (1) determine the value of x so that the volume of the shape is 165cm cube, and (2) once you have foun

d the value of x, determine the surface are if the shape. Be sure to show all steps and details of how you found your answer.

Mathematics
1 answer:
Reika [66]2 years ago
7 0

Answer:

  • x = 5 cm
  • 248 cm²

Step-by-step explanation:

The volume of the solid with x=0 is the product of its length, width, and height:

  V0 = (10 cm)(3 cm)(8 cm) = 240 cm³

The volume of the cutout is the same:

  Vc = (x cm)(3 cm)(x cm) = 3x² cm³

Then the volume of the solid with the cutout is ...

  V1 = V0 -Vc = 240 cm³ - 3x² cm³

This is 165 cm³, so we have ...

  165 = 240 -3x²

  55 = 80 -x² . . . . . divide by 3

  x² = 80 -55 = 25 . . . . add x²-55

  x = √25 = 5 . . . . . take the square root

___

The surface area is the total of the front and back faces and the lateral area of all the faces between them. That lateral area is the product of the perimeter of the front (or back) face and the width (3 cm). The perimeter (p) is the total of all edge lengths around the front face:

  p = 10 + 8 + (10-x)/2 + x + x + x + (10-x)/2 + 8 = 36 +2x

For x=5, the perimeter is ...

  p = 36 +2·5 = 46

so the lateral area is ...

... la = (46 cm)(3 cm) = 138 cm².

The area of each of the front and back faces is the area of the overal rectangular shape (10 cm by 8 cm) less the area of the cutout (x² cm²). So, that face area is ...

  fa = 2×((10 cm)(8 cm) -(5 cm)²) = 2×(55 cm²) = 110 cm²

Then the total surface area is the sum of lateral area and face area:

  S = la + fa = 138 cm² + 110 cm² = 248 cm²

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Answer:  Need more points.

Step-by-step explanation:

If George's total point  is 5 less than susan's points then  George needs more points to  make up to susan or pass susan's points.

For example ,

g =  s - 5       where g is George's points and s is susan's point.  

As you can see for G to catch up with s you will need 5 more points.

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3 years ago
Tim's bean sprout grew 3/ inches. Teegan's bean sprout grew 2 3/4 inches. How many more inches did Tim's bean sprout grow than T
ki77a [65]

Answer:

Tim's bean sprout grow by more than \frac{5}{8} \text{ inches}.

Step-by-step explanation:

We are given that Tim's bean sprout grew 3 3/8 inches. Teegan's bean sprout grew 2 3/4 inches.

We have to find how many more inches did Tim's bean sprout grow than Teegan's.

Firstly, converting both the mixed fractions in improper fraction get;

Tim's bean sprout grew = 3\frac{3}{8} = \frac{27}{8} \text{ inches}

Teegan's bean sprout grew = 2\frac{3}{4} = \frac{11}{4} \text{ inches}

Since the denominator of both the fractions is not the same, so we can't compare them both as which is larger or smaller.

Tim's bean sprout grew = \frac{27\times 1}{8\times 1} = \frac{27}{8} \text{ inches}

Teegan's bean sprout grew = \frac{11 \times 2}{4\times 2}=\frac{22}{8} \text{ inches}

Now, we can clearly see that Tim's bean sprout grew more than Teegan's bean sprout.

So, Tim's bean sprout grow by more than = \frac{27}{8}- \frac{22}{8} = \frac{5}{8} \text{ inches}

Hence, Tim's bean sprout grow by more than \frac{5}{8} \text{ inches}.

8 0
3 years ago
A small theater sold 72 tickets for a play. The ratio of adult tickets to child tickets was 4:1. The ratio of adult tickets to s
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Answer:

Adult 36

Children 9

senior 27

Step-by-step explanation:

We have 3 types of tickets as seen from the question;

Adult, children and seniors tickets.

Now, looking at the question critically,

Since the ratio of adults to children and senior citizens stands at 4: a specific value, we can then conclude that the ratio of tickets sold is 4:1:3

where 1 and 3 represents the ratio for the children and seniors respectively

So let’s calculate the individual ratio now.

For the total, we have 4 + 1 + 3 = 8

Thus, for the adults, we have 4/8 * 72 = 36

For the children, we have 1/8 * 72 = 9

For the seniors, we have 3/8 * 72 = 27

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3 years ago
A central angle theta in a circle of radius 7 m is subtended by an arc of length 8 m. Find the measure of theta in degrees. (Rou
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Answer: In degrees , The measure of \theta=65.5^{\circ}

In radians , the measure of  \theta =\dfrac{8}{7}\text{ radians}.

Step-by-step explanation:

We know that the formula for length of arc is given by :-

l=\theta r

, where \theta = Central angle subtended by arc.

r= radius of the circle.

As per given , we have

Radius of circle : r=7 m

Length of arc : l=  8 m

Substitute these values in the above formula , we get

8=\theta (7)\\\\\Rightarrow\ \theta =\dfrac{8}{7}\text{ radians}

Hence, the measure of \theta =\dfrac{8}{7}\text{ radians}.

To convert it into degrees we multiply it with \dfrac{180^{\circ}}{\pi}

The measure of \theta =\dfrac{8}{7}\times\dfrac{180^{\circ}}{\pi}

=(\dfrac{8\times180}{7\times3.14})^{\circ}=65.5141037307^{\circ}

\approx65.5^{\circ}

Hence, the measure of \theta=65.5^{\circ}

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