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3 years ago

Find the volume of the prism

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Answer:

440cm³

Step-by-step explanation:

Area of trapezium base=

$\frac{1}{2} \times (a + b) \times h$

$\frac{1}{2} \times (8 + 14) \times 4$

$\frac{1}{2} \times 22 \times 4 \\ = \frac{88}{2} \\ = 44 {cm}^{3}$

Volume=Area or trapezium x Height between trapezium ends

$= 44 \times 10 \\ = 440 {cm}^{3}$

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I need help.....Which values are possible lengths for segments AC and CD, respectively?

zavuch27 [327]

Given:

Given that R is a circle.

The length of BC is 5 units.

The length of CE is 12 units.

We need to determine the lengths of AC and CD.

Length of the chord AD:

The lengths of the segments AC and CD can be determined using the intersecting chords theorem.

Applying the theorem, we have;

$AC \cdot CD=BC \cdot CE$

Substituting the values, we have;

$AC \cdot CD=5 \times 12$

$AC \cdot CD=60$

Hence, when multiplying the two segments AC and CD, we get 60 units.

Thus, the length of the chord AD is 60 units.

Option F: 6 and 10

The possible lengths of AC and CD can be determined by multiplying the two segments.

Thus, we have;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=6 \times 10$

$60=60$

Thus, the possible lengths of AC and CD are 6 and 10 respectively.

Hence, Option F is the correct answer.

Option G: 8 and 9

Similarly, we have;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=8 \times 9$

$60 \neq 72$

Since, both sides of the equation are not equal, Option G is not the correct answer.

Option H: 7 and 14

Similarly, we have;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=7 \times 14$

$60 \neq 98$

Since, both sides of the equation are not equal, Option H is not the correct answer.

Option J: 12 and 13

Similarly, we have;

$AD=AC \cdot CD$

Substituting the values, we have;

$60=12 \times 13$

$60 \neq 156$

Since, both sides of the equation are not equal, Option J is not the correct answer.

Therefore, the possible lengths for segments AC and CD are 6 and 10 respectively.

Hence, Option F is the correct answer.

4 0

3 years ago

Read 2 more answers

Can anyone help???????????

Vedmedyk [2.9K]

Given:

The distance between the two buildings on a map = 14 cm

The scale is 1:35000.

To find:

The actual distance in km.

Solution:

The scale is 1:35000.

It means 1 cm on map = 35000 cm in actual.

Using this conversion, we get

14 cm on map = $14\times 35000$ cm in actual.

= $490000$ cm in actual.

= $4.9\times 1000o0$ cm in actual.

= $4.9$ km in actual. $[1\text{ km}=100000\text{ cm}]$

Therefore, the actual distance between two buildings is 4.9 km.

5 0

2 years ago

If a 24-foot ladder makes a 58 degree angle with the ground, how many feet up a wall will it reach? Round your answer to the nea

mash [69]

Answer: 20.4 feet

Step-by-step explanation:

(image attached for reference)

To find how high the ladder reaches on the wall, first find the relationship between the angle and the wall. The wall is opposite to the angle, so it's possible to solve this equation using sin(58). Sine equals opposite over hypotenuse so sin(58) = x/24. Multiply 24 on both sides to get an equation that can be plugged into a calculator of 24sin(58) = x.

24sin(58) = 20.35, which gets rounded up to a final answer of 20.4 feet.