All categories

3 years ago

Please help. no links. need answers for all questions :))

Mathematics

1 answer:

Bess [88]3 years ago

8 0

Answer:

1. The surface area of the cube is 324 square units

The volume of the cube 360 unit cube

2. The surface area of the cylinder is approximately 169.65 square units

The volume of the cylinder is approximately 169.65 unit cube

3. The surface area of a square pyramid is 360 square units

The volume of the square pyramid is 400 unit cube

4. The surface area of a cone is approximately 452.39 square units

The volume of the cone is approximately 50.27 unit cube

5. The surface area of the triangular prism is 240 square units

The volume of the triangular prism is 180 unit cube

6. The surface area of the sphere is approximately 804.25 square units

The volume of the sphere is approximately 2.144.66

7. The surface area of the composite figure is approximately 653.46 square units

The volume of the composite figure is approximately 1,474.45 unit cube

Step-by-step explanation:

1. The surface area of the figure, SA = 2 × (w·h + l·w + h·l)

Where;

w = The width of the figure = 6

l = The length of the figure = 12

h = The height of the figure = 5

We get;

SA = 2 × (6 × 5 + 12 × 6 + 5 × 12) = 324

The surface area of the figure, SA = 324

The volume of the figure, V = l × w × h

∴ V = 12 × 6 × 5 = 360

The volume of the figure, V = 360

2. The surface area of a cylinder, SA = 2·π·r² + 2·π·r·h

The radius of the given cylinder, r = 3

The height of the given cylinder, h = 6

∴ SA = 2×π×3² + 2×π×3×6 ≈ 169.65

The surface area of the cylinder, SA ≈ 169.65

The volume of a cylinder, V = π·r²·h

∴ V = π×3²×6 ≈ 169.65

The volume of the cylinder, V ≈ 169.65

3. The surface area of a square pyramid, SA = b² + 4·(1/2)·b·√((b/2)² + h²)

Therefore, for the given square pyramid, we have;

SA = 10² + 4×(1/2)×10×√((10/2)² + 12²) = 360

The surface area of a square pyramid, SA = 360

The volume of a square pyramid, V = (1/3) × Area of Base × Height

Therefore, or the given pyramid we have;

V = (1/3) × 10² × 12 = 400

The volume of the square pyramid, V = 400

4. The surface area of a cone, SA = π·r·(r + l)

Where;

The radius of the cone = r

The slant height of the cone, l = 10

The height of the cone, h = 6

∴ The radius of the cone, r = √(10² - 6²) = 8

∴ SA = π×8×(8 + 10) ≈ 452.39

The surface area of a cone, SA ≈ 452.39

The volume of the cone, V = (1/3) × π·r·h

∴ V = (1/3) × π × 8 × 6 ≈ 50.27

The volume of the cone, V ≈ 50.27

5. The surface area of the triangular prism, SA = 2 × (1/2)× b·h + b·w + h·w + w·l

Where;

b = The base length of the triangular surfaces = 5

h = The height of the triangular surfaces = 12

w = The width of the triangular prism = 6

l = The slant length of the prism = 13

Therefore;

SA = 2 × (1/2)× 5 × 12 + 5 × 6 + 12 × 6 + 6 × 13 = 240

The surface area of the triangular prism, SA = 240

The volume of a triangular prism, V = (1/2)·b·h·w

V = (1/2) × 5 × 12 × 6 = 180

The volume of the triangular prism, V = 180

6. The surface of a sphere, SA = 4·π·r²

Where;

r = The radius of the sphere = 8

∴ SA = 4 × π × 8² ≈ 804.25

The surface area of the sphere, SA ≈ 804.25

The volume of a sphere, V = (4/3)·π·r³

∴ V ≈ (4/3)×π×8³ ≈ 2,144.66

The volume of the given sphere, V ≈ 2.144.66

7. The figure is a composite figure made up of a cone and an hemispher

The surface area of the cone shaped part of the figure, SA = π·r·l

Where;

r = The radius of the cone = 8

l = The slant height of the cone = 10

∴ SA₁ = π × 8 × 10 ≈ 251.34

The surface area of the cone shaped part of the figure, SA₁ ≈ 251.34

The volume of the cone, V₁ = (1/3)·π·r²·h

Where;

h = The height of the cone = √(10² - 8²) = 6

∴ V₁ = (1/3) × π × 8² × 6 ≈ 402.12

The volume of the cone, V₁ ≈ 402.12

The surface area of the hemisphere, SA₂ = 2·π·r²

∴ SA₂ = 2 × π × 8² ≈ 402.12

The surface area of the hemisphere, SA₂ ≈ 402.12

The volume of a hemisphere, V₂ = (2/3)·π·r³

∴ V₂ = (2/3) × π × 8³ ≈ 1072.33

The volume of a hemisphere, V₂ ≈ 1,072.33

The surface area of the composite figure, SA = SA₁ + SA₂

∴ SA = 251.34 + 402.12 = 653.46

The surface area of the composite figure, SA ≈ 653.46

The volume of the composite figure, V = V₁ + V₂

∴ V = 402.12 + 1,072.33 = 1,474.45

The volume of the composite figure, V ≈ 1,474.45.

You might be interested in

What property is shown: -7 x 1 = -7

noname [10]

Answer:

multiplicative inverse

Step-by-step explanation:

7 0

3 years ago

A large restaurant is being sued for age discrimination because 15% of newly hired candidates are between the ages of 30 years a

lesya [120]

Answer:

Part A:

The null and alternative hypothesis are:

$H_0: \pi=0.5\\\\H_1: \pi\neq 0.5$

Part B:

- A Type I error is when the null hypothesis is rejected although it is true. In this case, it would mean that we conclude that the hiring process is discriminatory, when in reality it is a random result and the process is not discriminatory.

- A Type II error is when the null hypothesis fails to be rejected although it is false. In this case, the hiring process is discriminatory, but statistically the result is not significant enough to prove that.

Part C:

A reduction in the significance level causes a reduction in the power of the test.

Part D:

The power of the test is increased with a larger sample.

Step-by-step explanation:

We have a restaurant with hire a proprotion of 15 % of people in the age ragne of 30-50 years. The expected proportion, according to the applicants, is 50%.

The test will tell us if the actual 15% is a result of a discriminatory practice or a random result.

Part A:

The null and alternative hypothesis are:

$H_0: \pi=0.5\\\\H_1: \pi\neq 0.5$

Part B:

Part C:

The power of an hypothesis test is the probability that the test rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true.

If the significance level is reduced (from 5% to 1%), the rejection region is reduced, so the probability of rejecting the null hypothesis is also reduced.

Then, a reduction in the significance level causes a reduction in the power of the test.

Part D:

A bigger sample size gives robustness to the sample statistic. Then, if the alternative hypothesis is true, the probabilities of detecting the effect are increased with increased sample size.

Then, the power of the test is increased with a larger sample.

3 0

3 years ago

rosa made a Mosaic while using 42 black tiles 35 blue tiles and 23 red tiles write a percent to represent the number of red tile

Vlada [557]

23% because (42+35)+23=100. 42+35=77. 100-77=23.

4 0

3 years ago

Helppppppppppppppppppppppppppppppppppppppppppppppp

Maslowich

i belive it is xy^2 but tell me if ou need more

3 0

3 years ago

Read 2 more answers

the sales tax in one town is 8% so the total cost of an item con be written as c plus 0.08c what is the total cost of an item th

Anastasy [175]

Answer:

$12.96

Step-by-step explanation:

The cost of the item = $12.00

The tax on the item = 12 times 0.08 =$0,96

So the total cost = $12.00 plus $0.96 = $12.96

5 0

3 years ago