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kolezko [41]
3 years ago
14

5. What is the volume of the geometric solid produced by the triangle below when it is

Mathematics
1 answer:
IgorLugansk [536]3 years ago
5 0

The diagram of the triangle is missing, so i have attached it.

Answer:

Surface area = 9.425 sq.units

Step-by-step explanation:

When a triangle having an interior angle as 30°, 60° or 90° is rotated, then a cone is formed.

Thus, we need to find the surface area of the cone.

Surface area of a cone is πr ² + πrL

where;

r = radius of the cone

L = slant height of the cone

I have attached the cone formed as the second image.

Looking at the image of the cone, we need to find the radius and slant height.

From the triangle image, we can use trigonometric ratios;

tan 30 = BC/AB

In surd form, BC/AB = 1/√3

Thus, BC is equivalent to 1 and AB equivalent to √3

Using Pythagoras theorem, we can find AC.

(AC)² = (AB)² + (BC)²

AC = √[(AB)² + (BC)²]

AC =√[(√3)² + (1)²]

AC = √[3 + 1]

AC = √4

AC = 2

So, radius, r corresponds to BC = 1

And slant height L corresponds to AC = 2.

Thus,r = 1 and L = 2

So,

Surface area of cone = π(1)² + π(1)(2) = π + 2π = 9.425 sq.units

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Does anyone know how to do this ?
goldenfox [79]

Answer: D) 32

Step-by-step explanation:

The area of a parallelogram equals its base times its height. Substitute the base and area into this formula to solve for the height:

A=bh

40=(5)(h)

h=8

If ABCD is a parallelogram, opposite sides are parallel, so AB is parallel to DC. If AB is parallel to DC, EB is parallel to DC. Since EB is parallel to DC, quadrilateral EBCD has at least one pair of parallel sides, making it a trapezoid. The area of a trapezoid is equal to \frac{h(b_{1}+b_{2})  }{2} where h is the height, b_{1} is one base, and b_{2} is the other base. Plug the necessary values into the formula:

A=\frac{h(b_{1}+b_{2})  }{2}

b_{1} =AB-AE\\DC=AB\\b_{1} =DC-AE\\b_{1} =5-2\\b_{1} =3

b_{2} =5

h=8

A=\frac{8(3+5)}{2}

A=32

The answer is D) 32.

6 0
2 years ago
Can someone help. Write a word problem about equal groups and act it out to solve
Alona [7]

Answer:

HOPE THAT MAY HELP YOU :)

Step-by-step explanation:

Equal groups are illustrations of using the same variable.

A word problem that uses equal group is:  

Christopher traveled a distance of 5 miles yesterday; he traveled a distance of 4 miles earlier today. Calculate the total distance traveled  

The only condition for equal groups is that:  

The units or variable must be the same  

For instance:

Add 5 miles and 4 miles ----- This represents distance

Remove 2 liters from 7 liters --- This represents volume

Add 5 hours and quarter of an hour -- This represents time

And so on.

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What is the volume that can fit exactly 128 cubes with 1/2 inch sides?
aleksandrvk [35]
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Chin canned a number of quart jars anf a number of pints jars of tomatoes from hid garden. A pint is 16 onces and a quart is 32
ryzh [129]

Answer:

The equation which models the scenario is:   16 p + 32 q  = 1280

Step-by-step explanation:

The total number of pints packed  = p

The total number of quarts  packed  = q

The weight of 1 pint jar of tomatoes  = 16 oz

So, the total weight of p pints  = p x ( Weight of 1 pint) = p x ( 16 oz) = 16 p

The weight of 1 quart jar of tomatoes  = 32 oz

So, the total weight of q quarts  = q x ( Weight of 1 quart) = q x ( 32 oz)

= 32 q

Now, the TOTAL WEIGHT of p pints and q quarts

= Total weight of { p pints +  q quarts}  = 16 p + 32 q

Also, chin canned a total of 1280 ounces.

⇒ TOTAL WEIGHT of p pints and q quarts = 1280 ounces

or,   16 p + 32 q  = 1280 ounces

Hence, equation which models the scenario is:   16 p + 32 q  = 1280

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3 years ago
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