A pyramid and a cone are both 8 centimeters tall and have the same volume.
What statement must be true about the two solids?
АЛ
A. The vertical cross-sections of the prisms at the same width must
have the same area.
B. The area of the cross-sections of the prisms are multiples of each
other.
C. The cross-sections of the prisms are the same shape.
D. The horizontal cross-sections of the prisms at the same height
must have the same area.
Answers
Answer:
D. The horizontal cross-sections of the prisms at the same height must have the same area.
Step-by-step explanation: I dont know what the guy above is saying but this is the right answer
Since it is given that both prisms have the same height and volume, the answer is option D. The horizontal cross-sections of the prisms at the same height must have the same area.
A solid figure is one which has surface area and volume. Examples are prisms, cube, cuboid etc. Thus cones and pyramids are solid figures.
From the given question,
Volume of a cone, V = [tex]\frac{1}{3}[/tex][tex]\pi r^{2} h[/tex]
where r is its radius, and h its height
also,
Volume of a pyramid, V = [tex]\frac{1}{3}[/tex] lwh
where l is its length, w is the base width and h is its height.
Given that: i. volume of cone = volume of pyramid
ii. height of cone = height of pyramid
Then,
[tex]\frac{8}{3}[/tex][tex]\pi r^{2}[/tex] = [tex]\frac{8}{3}[/tex]lw
[tex]\pi r^{2}[/tex] = lw
Thus it can be deduced that at the same height, the horizontal cross section of the prisms have equal area. So that option D is the appropriate answer to the given question.
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Related Questions
does anyone know how to solve this problem?
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Help me with this please!!!!!!!!
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Answer:
I guess it is a rectangle
HELP !!!!!!!!!!!!!!!!
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The perimeter of the triangular park shown on the right is 12x - 1. What is the missing length?
Answers
Answer:
6x-4
Step-by-step explanation:
c-the missing length
(2x+5)+(4x-2)+c = 12x-1
2x+5+4x-2+c=12x-1
6x+3+c=12x-1
6x+4+c=12x =>4+c=12x-6x =>4+c=6x => c=6x-4
What is the missing length? 6x-4
PLEASE HELP THIS IS OVERDUE!!
Answers
Answer:
y=1/2x-3
Step-by-step explanation:
Can you conclude from the figure that ABC is similar to DEF? Explain.
Answers
Answer:
Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.
Step-by-step explanation:
We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.
Triangle ABC:
Measure of angle A= 60°
Measure of angle C= 40°
Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°
Triangle DEF
Measure of angle E= 80°
Measure of angle F= 40°
Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°
The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.
The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.
Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.
there are 5 green balls, 1 yellow ball,and 4 red balls in a bag. what are the probabilities?
choosing a red:
not choosing yellow:
choosing a blue:
Answers
Answer:
it is green balls=5
red balls =4
red +green
5+9
=14
Translate algebraic words to symbols.
Two times the sum of a and b
A. 2(a + b)
B. 2 + ab
C. 2ab
D. 2(a/b)
Answers
Answer:
Option A
Step-by-step explanation:
That is your answer
Answer:
a) 2(a+b)
Step-by-step explanation:
the sum of 2 numbers (or more) is always addition
so the sum of a and b would be (a+b)
then, 2 times of a and b;
2(a+b)
^the times sign between the bracket and the 2 isnt needed, whenever there is a bracket and a number next to it, it is automatically a multiplication.
please, help me with this fast!! I'm giving points!!!!
Answers
Answer:
Step-by-step explanation:
c circle
Need help on this problem!!
Answers
100+225=325
The square root of 325 is 18.0277563773 is you round it to the hundredths place it’s 18.03
In how many different ways can 3 people select seats at a
dining table having 8 seating positions if they can select any
seat?
Answers
Dana is planning the school picnic and needs to decide what food vendor to
use. She asks 750 students whether they would rather have a taco truck or a
fruit smoothie cart. The results of the survey are shown in the table.
Taco truck Fruit smoothies Total
120
300
Eighth-graders 180
Ninth-graders 110
90
200
Total
290
210
500
What is the relative frequency of eighth-graders who want fruit smoothies?
26
Answers
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Consider the following set of equations:
Equation M: y = x + 8
Equation P: y = 3x + 6
Which of the following is a step that can be used to find the solution to the set of equations? (4 points)
a
x = 3x + 6
b
x + 8 = 3x + 6
c
x + 6 = 3x + 8
d
x = 3x
Answers
Answer:
B. X+8=3x+6
Step-by-step explanation:
You substitute the y value of one equation with the y value of the 2nd equation.
A fighter jet has traveled 60 miles since take-off. The equation
194. – 60 can be used to determine the total number of miles
the jet has traveled. In the equation, y represents the number of
miles traveled, and I represents the number of minutes traveled.
Which statement best describes the rate of change in the distance
traveled?
A.For every 1 minute, a fighter jet travels 38 miles.
B.For every 1 minute, a fighter jet travels 19 miles.
C. For every 1 second, a fighter jet travels 19 miles.
D.For every 28 minutes, a fighter jet travels 115 miles.
Answers
Answer:
C. For every 1 second, a fighter jet travels 19 miles.
Step-by-step explanation:
PLEASE HELP ME I REALLY NEED THIS
Tony made 14 decorations for the class party. He made 8 times as many decorations as Jack did, but he lost 2. Which equation could be used to find the number of decorations & Jack
made?
O 8x + 2 = 14
O 8 - 2 = 14
O2 + 8 = 14
O 22-8 = 14
Answers
Answer:
It is either a or b. since 8-2 does not equal 14, and 8+2 does not equal 14. I think it is most likely to be a though.
Step-by-step explanation:
What is the axis of symmetry of h(x) = –2x2 + 12x – 3?
a. x = –15
b. x = –3
c. x = 3
d. x = 15
Answers
We will see that the axis of symmetry is x = 3, so the correct option is c.
How to find the axis of symmetry of a quadratic function?
The axis of symmetry is a line of the form x = a, such that it divides the parabola in two halves.
Particularly, the axis of symmetry passes through the vertex, so the x-value of the vertex is equal to the value of the axis.
Then we only need to find the x-value of the vertex, remember that for a quadratic:
[tex]y = a*x^2 + b*x + c[/tex]
The vertex is at:
[tex]x = -b/2a[/tex]
Then in our case, the vertex is at:
[tex]x = -12/(2*-2) = -12/-4 = 3[/tex]
So the axis of symmetry is x = 3, then the correct option is C.
If you want to learn more about quadratic equations:
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Lucy is planting grass in her front yard and backyard. Her front yard is 20 ft. by 35 ft., and her backyard is 13 ft. by 17 ft. What is the total area of the space in which Lucy will plant grass?
Answers
13x17=221
20x35=700
Help please I am struggling thank you
Answers
The answer is 904.8 yd³
Step-by-step explanation:
The formula for a sphere's volume is 4/3πr²
r in this case is 12/2 which is 6. That means that r=6 which gives us 904.78 which is rounded to 904.8.
Answer:
904.32
Step-by-step explanation:
v= [tex]\frac{4}{3\\}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
first cube the radius (6) (radius is half of the diameter 12)
6x6x6 = 216
multiply by pi
216 x 3.14 = 678.24
multiply by 4/3
[tex]\frac{678.24}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{2712.96}{3\\}[/tex] = 904.32
You buy a car for $16,000. It will decrease in value by 10% each year. How much will it be worth after 4 years?
Answers
Answer: 9,600
Step-by-step explanation:
I could possibly did wrong but I shall explain this none the less. I first knew that 10% of 16,000 was 1,600. So then I just timed that by four getting 6,400. I then did 16,000-6,400 getting $9,600. Sorry if I’m wrong
Answer:
$9600
Step-by-step explanation:
10% of 16,000 = 1600
1600*4= 6400
16,000-6,400
= 9600
who is the first test tube baby of nepal
Answers
After that incident, the Civil defense team decided to buy new trucks with ladders higher than 100 feet. They found 2 different trucks with the same height of ladders. The first truck costs $145,000 and will cost $0.31 per mile traveled based on the current gas prices. The second truck will cost $160,000 but gets better gas mileage, costing $0.27 per mile. They need to decide which truck is the best deal.
Answers
Answer:
the first truck
Step-by-step explanation:
the cost difference between the first truck and the second truck = $160,000-$145,000 = $15,000
the difference of gas cost between the first truck and the second truck = $0.31 - $0.26= $0.05 per mile.
so,
I think, this is a very significant number of truck cost compared with gas cost
for the best deal, the first truck is the best choice.
how to solve y=-5/2x+4, Y=-1 using substitution
(i need the steps not just the answer)
Answers
Answer:
Step-by-step explanation:
- Since y = -1, we will substitute the y variable in the equation for -1.
-1 = -5/2x + 4
- Take away 4 from both sides in order to find out what x equals so we can substitute it.
5 = -5/2x
- turn it into a positive by multiplying each side by -1.
-1(-5 = -5/2x) =
5 = 5/2x
- Divide each side by 5.
1 = 1/2x
- Multiple both sides by 2.
2 = x
- Substitute the variables.
x = 2
y = -1
-1 = -5/2(2) + 4
Please helpppp
Extra points and brainleist
Answers
Answer:
B
Step-by-step explanation:
x² - 4x - 7 = 0
(x - 2)² = 11
PLS HELP ASAP
Function g is shown on the graph
Which function represents g
Answers
Answer:
Step-by-step explanation:
Can someone please help me on this please I beg you no links I really appreciate it plz
Answers
PLEASE I NEED HELP ASAP!!
Answers
Answer:
8√2
Step-by-step explanation:
How to write 8^5 x 8^6 as a single power
Answers
Step-by-step explanation:
We know that
[tex]\boxed{\sf a^m\times a^n=a^m+n}[/tex]
[tex] \sf \: {8}^{5} \times {8}^{6} \\ \sf \leadsto \: {8}^{5 + 6} \\ \sf \leadsto {8}^{11} [/tex]
[tex]\sf More\;to\: know{\begin{cases}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{cases}}[/tex]
SOMEONE PLEASEEEE HELPPPP?!?!?!?!!?
Answers
Answer:
Step-by-step explanation:
Top/Bottom = 12
Sides = 15
Front/Back = 20
20 + 15 + 12 = 47
47 / 1/2 = 23.5
for brainiest:):):):):):):)
Answers
Answer:
I'm pretty sure 1 is verticle and 2 is complimentary
Step-by-step explanation:
pls help!!
1. 5n + 10 = 20 n = ?
2. 36 = 12m m = ?
3. 4a - 12 = 28 a = ?
4. q/5 = 10 q = ?
Answers
Answer:
here you go! :))
n= 2
m=3
a= 10
q= 50