1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Flura [38]
3 years ago
12

Use the following image to answer the questions below. The base is a regular pentagon and the vertex is directly above the cente

r of the base:
a. If you knew the dimensions of this solid, how would you calculate the surface area?
b. How would you calculate the volume?
c. How does the volume of this pentagonal pyramid compare to the volume of a prism with a congruent pentagonal base and a congruent height?
d. What cross-sectional shapes, regular or irregular, could you get by cutting a plane through this figure? Explain your answer.

Mathematics
1 answer:
levacccp [35]3 years ago
7 0

a. The lateral area is the area of 5 congruent triangles. The strategy for computing their area will depend on the dimensions given. There are methods for computing triangle area based on side lengths, base length and height, coordinates of the points, and other dimensions. One straightforward way, given the appropriate dimensions is to multiply the slant height by the perimeter of the base, then divide that product by 2.


The base area is that of 5 congruent triangles. Again, their total area can be computed from half the product of the perimeter of the base and the apothem (height of the triangle).


The total surface area is the sum of lateral area and base area.


For example, given the apothem of the base (a) and the slant height of the side face (s), the total surface area (A) will be

... A = 5·a·tan(36°)·(a + s)


b. The volume is conventionally calculated as 1/3 of the product of the base area (B) and the height (h).

... V = (1/3)Bh


c. The volume of a prism with the same base area and height will be

... V = Bh

The volume of a pyramid is 1/3 of that.


d. A plane can intersect this pyramid to form a triangle, rectangle, trapezoid or other irregular quadrilateral, pentagon, or hexagon. The number of edges the cross-section has depends on the number of faces (including the base) the plane cuts. That number can be 3 through 6.

You might be interested in
Rationalise 1/√5 please tell​
Assoli18 [71]

Answer:

Step-by-step explanation:

1/\sqrt{5}

=1\sqrt{5} *\sqrt{5}/\sqrt{5}

=1*\sqrt{5}/\sqrt{5}*\sqrt{5}

=1\sqrt{5}/5

6 0
3 years ago
There are many cylinders with radius 6 meters. Let h represent the height in meters and V represent the volume in cubic meters.
KiRa [710]

The equation that represents the volume of the cylinder is 36πhhh m³.

Explanation:

Formula: volume of a cylinder = πr²h

pi =  π = 22/7

r = radius

6² πhhh

36πhhh m³

4 0
2 years ago
using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equ
natita [175]

Answer:

The projected population in 2026 is of 699.3 million.

Step-by-step explanation:

Population:

The population, in x years after 2000, is given by the follwing equation:

y - 4.55x = 581

That is:

y(x) = 4.55x + 581

What is projected population in 2026?

2026 - 2000 = 26, so this is y(26).

y(26) = 4.55(26) + 581 = 699.3

The projected population in 2026 is of 699.3 million.

5 0
3 years ago
Alia has swimming class every fourth day and diving class every sixth day. If she had swimming class and diving class on 5 june,
dolphi86 [110]

Answer:

June 17

Step-by-step explanation:

the least common multiple of 4 and 6 is 12.  Add 12 to June 5 and you get June 17

3 0
2 years ago
If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.
Neporo4naja [7]

Answer:

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

<em></em>

Step-by-step explanation:

Given

f(x)=x^3-12x^2+35x-24

f(8) = 0

Required

Find all zeros of the f(x)

If f(8) = 0 then:

x = 8

And x - 8 is a factor

Divide f(x) by x - 8

\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}

Expand the numerator

\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}

Rewrite as:

\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}

Factorize

\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}

Expand

\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}

Factorize

\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}

\frac{f(x)}{x - 8} = (x - 1)(x - 3)

Multiply both sides by x - 8

f(x) = (x - 1)(x - 3)(x - 8)

<em>Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)</em>

7 0
2 years ago
Other questions:
  • You randomly survey students in your school about the color of their eyes. The results are shown in the tables. For each gender,
    10·1 answer
  • Which could be the area of the face of the rectangular prism
    12·2 answers
  • Is(5, 6)asolutiontotheinequality<br> y &lt; 2x + 4 ?
    15·1 answer
  • Simplify 25/100 eiejevskkehs
    12·2 answers
  • Which is a quadratic function?<br><br> A. 3x+y^2=5<br> B. y=3x+5<br> C. x=3y+5<br> D. 3x^2+y=5
    7·1 answer
  • What is the pair of angles called.
    13·1 answer
  • A man invests 10000 for 3 years at a certain rate of interest, compounded annually. At the
    12·2 answers
  • Sin 0 =(8)/(9), tan 0 &gt;0<br> find sec 0
    5·1 answer
  • A fruit basket is filled with 8 bananas, 3 oranges, 5 apples, and 6 kiwis.
    12·1 answer
  • A pair of equations is shown below.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!