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
jolli1 [7]
3 years ago
6

A cube of sides 10cm was cut across to obtain a prism. Calculate the surface area of the prism and the volume of the prism

Mathematics
1 answer:
hodyreva [135]3 years ago
4 0

Answer:

Part A

The volume of the triangular prism is 500 cm³

Part B

The total surface area of the prism is approximately 441.42 cm²

Step-by-step explanation:

The given details are;

The dimensions of the side length of the cube, s = 10 cm

The shape the cube was cut across to obtain = A prism

Part A

Whereby the prism obtained is a triangular prism, we have;

The cube can be cut in half to form a triangular prism

The volume of each triangular prism obtained = (1/2) × The volume of the cube

∴ The volume of the triangular prism = (1/2) × (10 cm)³ = 500 cm³

Part B

The height of the prism, h = 10 cm × sin(45°) = 5·√2 cm = (1/2) × The base width of the prism

The triangular cross sectional area of the prism, A₁ = 5·√2 × 5·√2 = 50

The square cross sectional area, A₂  = 10 × 10 = 100

The cross sectional area of the base, A₃ = 10·√2 × 10 = 100·√2

The total surface area of the prism, A = 2·A₁ + 2·A₂ + A₃

∴ A = 2×50 + 2×100 + 100·√2 = 300 + 100·√2 ≈ 441.42

The total surface area of the prism, A ≈ 441.42 cm²

You might be interested in
A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 65 . What is the volume of the dilated prism?
mina [271]

Answer:

The volume of the dilated prism is 86.4ft^3.

Step-by-step explanation:

The original prism has base area 5ft^2 and a height of 10ft.

The volume of the original prism is v=5\times 10=50ft^3.

The prism is dilated by a scale factor of k=\frac{6}{5}.

To find the volume of the dilated prism, we multiply the volume of the original prism by k^3=\frac{216}{125}.

V=\frac{216}{125} \times 50ft^3

\Rightarrow V=86.4ft^3

3 0
2 years ago
PLEASE HELP
densk [106]

For this case we have that by definition, a function is of the form:

y = f (x)

So, we have the following system of equations:

y = -6x + 2\\y = -2x + 4

Equating the equations we have:

-6x + 2 = -2x + 4

Adding 2x to both sides of the equation:

-6x + 2x + 2 = 4\\-4x + 2 = 4

Subtracting 2 from both sides of the equation:

-4x = 4-2\\-4x = 2

Dividing between -4 on both sides of the equation:

x = \frac {2} {- 4}\\x = - \frac {1} {2}

Thus, the value of the variable "x" is -0.5.

Answer:

-0.5

6 0
3 years ago
Help me pleasee!!!!!!!!!!!!
tresset_1 [31]

Answer:

Step-by-step explanation:

Angles 1, 2, and 3 are supplementary (they add up to equal 180). If angles 1 and 3 are 20 each, then their sum in 40, making angle 2

180 - 40 = 140. If this central angle is 140 degrees, then the measure of the arc that it cuts off also measures 140 degrees. This is not to be confused with the arc length, which is not even remotely the same thing!

4 0
3 years ago
Pat made a total of 48 pottery plates and cups. if she made twice as many plates as cups, how many plates did she make?
ddd [48]
If C stands for cups, solve for C

48 - 2c = 0
    l
subtract 48 from each side.
    l
2c=-48
    l
divide 48 by 2 --->  24.



3 0
3 years ago
Read 2 more answers
Trigonometric identities: Performance task
MakcuM [25]

#1

\\ \sf\longmapsto (1+cosx)(1-cosx)

\\ \sf\longmapsto 1-cos^2x

\\ \sf\longmapsto sin^2x

#2

\\ \sf\longmapsto \dfrac{1}{cot^2x}-\dfrac{1}{cos^2x}

\\ \sf\longmapsto tan^2x-sec^2x

\\ \sf\longmapsto 1

3 0
3 years ago
Read 2 more answers
Other questions:
  • Line ET is tangent to circle A at T, and the measure of arc TG is 46. What is the measure of
    14·1 answer
  • Given that 9t-5=103, find the value of t
    13·1 answer
  • At a benefit​ concert, eleven bands have volunteered to perform but there is only enough time for eight of the bands to play. Ho
    12·1 answer
  • Bill has $6 more than Ted. Together they have $32. Write two equations and then solve for the amount of money that bill has.
    8·1 answer
  • If you had a bad day just know God was there with you, and u are never alone!:)
    13·1 answer
  • Lincoln wants the monthly payment for a $150,030 fixed mortgage to be $660 but his credit score is 650. What percent does Lincol
    13·1 answer
  • What is 0.94 rounded to the nearest tenth
    5·2 answers
  • Hi i hope ur sunday is going well. Please help me with this answer
    12·2 answers
  • I NEED HELP PLEASE.
    10·1 answer
  • Multiply. (−6/35)⋅14/27 What is the product? Enter your answer as a fraction, in simplified form, in the box.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!