1. For the pair of similar solids, find the value of the variable.
Cylinder 1: r = 15 cm, h = 6 cm
Cylinder 2: r = 5 cm, h = x cm
My answer: D) 2 cm
2. For the pair of similar solids, find the value of the variable.
Pyramid 1: h = 24 mm, b = x mm
Pyramid 2: h = 8 mm, b = 4 mm
My answer - A) 12 mm
3. A rectangular prism has a width of 92 ft and a volume of 240 ft^3. Find the volume of a similar prism with a width of 23 ft. Round to the nearest tenth, if necessary.
My answer - A) 3.8 ft^3
4. A pyramid has a height of 5 in. and a surface area of 90 in^2. Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if necessary.
My answer - A) 360 in^2
5. Find the surface area of a sphere with a radius of 12 m.
My answer- B) 804 cm^2
6. Find the surface area of a sphere with a radius of 12 m.
My answer - A) 1,809 m^2
7. Find the volume of the sphere with a radius of 4 ft.
My answer - C) 268 ft^2
^Are my answers correct?
#5 and 6 are the same question
#6 is correct
I worked #5 backwards, it is correct if r = 8
The last 4 are right, however I don't know about the others.
#1-3 are also correct
1. r1/r2 = 15/5 = 3.
h1/h2 = 3,
6/h2 = 3
h2 = 2 cm.
3. W1/W2 = 92/23 = 4.
V1/V2 = 4^3 = 64.
240/V2 = 64,
V2 = 3.8 Ft^3.
Dr. Mathematical = lue
1. To find the value of the variable in the given pair of similar solids, we can set up an equation using the ratios of the corresponding dimensions of the two solids. In this case, the ratio of the radii is 15 cm / 5 cm, and the ratio of the heights is 6 cm / x cm. Setting up the equation, we get:
15/5 = 6/x
Simplifying this equation, we have:
3 = 6/x
To solve for x, we can multiply both sides of the equation by x/6:
(x/6) * 3 = 6/x * (x/6)
x/2 = 1
Multiplying both sides by 2, we find:
x = 2 cm
So, the correct answer is D) 2 cm.
2. To find the value of the variable in this pair of similar solids, we can use the same method as in the previous question. The ratio of the heights is 24 mm / 8 mm, and the ratio of the bases is x mm / 4 mm. Setting up the equation, we get:
24/8 = x/4
Simplifying this equation, we have:
3 = x/4
To solve for x, we can multiply both sides of the equation by 4/1:
(x/4) * 3 = 4/1 * (x/4)
3x/4 = 4
Multiplying both sides by 4/3, we find:
x = 16/3 mm
So, the correct answer is not listed among the options provided. The correct answer is approximately 5.3 mm.
3. To find the volume of a similar prism with a different width, we can use the fact that the volume of a rectangular prism is proportional to the cube of its dimensions.
In this case, we have a rectangular prism with a width of 92 ft and a volume of 240 ft^3. Let's call the width of the similar prism x ft. Setting up the proportion, we get:
92^3 / 240 = x^3 / V2
Simplifying this equation, we have:
x^3 = (92^3 * V2) / 240
To find the volume of the similar prism, we substitute the width x into the volume formula for a rectangular prism, which is V = width * length * height. Since the length and height are proportional to the width, we can write:
V2 = (92 / x) * length2 * height2
Substituting this expression into the equation above, we have:
x^3 = (92^3 * 92 / x) / 240
Simplifying this equation, we get:
x^3 = (92^4 * 92) / (240 * x)
To solve for x, we can take the cube root of both sides:
x = cube root of [(92^4 * 92) / (240 * x)]
Using a calculator, we find:
x ≈ 23.03 ft
Rounding to the nearest tenth, the correct answer is A) 23.0 ft^3.
4. To find the surface area of a similar pyramid with a different height, we can use the fact that the surface area of a pyramid is proportional to the square of its dimensions.
In this case, we have a pyramid with a height of 5 in and a surface area of 90 in^2. Let's call the height of the similar pyramid x in. Setting up the proportion, we get:
5^2 / 90 = x^2 / A2
Simplifying this equation, we have:
25 / 90 = x^2 / A2
To find the surface area of the similar pyramid, we substitute the height x into the surface area formula for a pyramid, which is A = (1/2) * base * height + [(1/2) * base * slant height] (where slant height is calculated using the Pythagorean theorem). Since the base and slant height are proportional to the height, we can write:
A2 = (5 / x) * base2 * slant height2
Substituting this expression into the equation above, we have:
25 / 90 = x^2 / [(5 / x) * base2 * slant height2]
Simplifying this equation, we get:
25 / 90 = x^2 / [(5 / x) * base2 * slant height2]
To solve for x, we can take the square root of both sides:
x = square root of [(25 * (5 / x) * base2 * slant height2) / 90]
Using the given information, we can substitute values into the equation and calculate the surface area of the similar pyramid. However, the value of the base is not provided in the question, so we cannot calculate the surface area accurately. Therefore, the answer cannot be determined from the information given.
5. The surface area of a sphere is calculated using the formula A = 4πr^2, where r is the radius of the sphere. To find the surface area, we substitute the given radius of 12 m into the formula:
A = 4π * (12 m)^2
A ≈ 4π * 144 m^2
A ≈ 576π m^2
Using a calculator to approximate the value of π, we find:
A ≈ 576 * 3.14 m^2
A ≈ 1806.24 m^2
Rounding to the nearest whole number, the correct answer is A) 1806 m^2.
6. The surface area of the sphere is calculated using the formula A = 4πr^2, where r is the radius of the sphere. To find the surface area, we substitute the given radius of 12 m into the formula:
A = 4π * (12 m)^2
A ≈ 4π * 144 m^2
A ≈ 576π m^2
Using a calculator to calculate the value of π, we find:
A ≈ 576 * 3.14 m^2
A ≈ 1808.64 m^2
Rounding to the nearest whole number, the correct answer is A) 1809 m^2.
7. The volume of a sphere is calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. To find the volume, we substitute the given radius of 4 ft into the formula:
V = (4/3)π * (4 ft)^3
V = (4/3)π * 64 ft^3
V ≈ 268.08 ft^3
Rounding to the nearest whole number, the correct answer is C) 268 ft^3.
Overall, the answers you provided for questions 1, 2, and 7 are correct. However, the answers for questions 3, 4, 5, and 6 are different from the correct answers.