A glass vase weighs 0.12lb, how much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large?

possible answers;
4.32lbs
25.92lbs
0.72lbs
155.52lbs

These are the last problems I have and I can't figure them out can someone please help me?

The volume of a sphere is 5,000pim^3. What is the syrface area of the sphere to the nearest square meter?
possible answers;
3,033mm^2
62,832m2
195m^2
1,517m^2

Find the surface are of a sphere with a circumference of 155mm. Round to the nearest tenth.
possible answers;
7,647.4mm^2
608.6mm^2
24.7mm^2
3,823.7mm^2

Can someone please help me?

Since the mass (weight) is related to its volume

and the volumes of similar objects are proportional to the cube of their sides ....

w/.12 = 6^3/1^3
w = .12(216)/1 = 25.92

2nd question:

V of sphere = (4/3)πr63
(4/3)πr^3 = 5000π
(4/3)r^3 = 5000 , I divided both sides by π
r^3 = 5000(3/4) = 3750
r = cuberoot(3750) = appr. 15.536..
SA = 4πr^2
= 3033 m^2 to the nearest whole number

(your answer has mm^2, it should be m^2, probably your typo )

3rd: try it yourself

hint: C = 2πr
2πr = 155 , solve for r and use the 2 formulas from above

I believe the answer for the 3rd one is 7,647.4 if I did it right

Sure, I'd be happy to help you! Let's start with the first problem:

1. A glass vase weighs 0.12lb, and we need to find the weight of a similarly shaped vase of the same glass if each dimension is 6 times as large.

To solve this, we need to consider that the weight of an object is proportional to its volume. Since the vases are similarly shaped, we can use the concept of volume ratio to find the weight of the larger vase.

Since each dimension is 6 times as large, the volume of the larger vase will be equal to (6^3) = 216 times the volume of the original vase.

So, if the weight of the original vase is 0.12lb, then the weight of the larger vase is:

0.12lb * 216 = 25.92lbs

Therefore, the correct answer is 25.92lbs.

Let's move on to the next problem:

2. The volume of a sphere is given as 5,000πm^3, and we need to find the surface area of the sphere to the nearest square meter.

The surface area of a sphere can be found using the formula:

Surface Area = 4π(radius)^2

To find the radius, we can rearrange the formula for volume of a sphere:

Volume = (4/3)π(radius)^3

Rearranging this formula, we get:

(radius)^3 = (3/4π) * Volume

(radius)^3 = (3/4π) * 5000π = 37500

Taking the cube root of both sides, we get:

radius ≈ ∛(37500) ≈ 34.64m

Plugging this radius into the formula for surface area, we get:

Surface Area = 4π(34.64)^2 ≈ 1517m^2

Therefore, the correct answer is 1,517m^2.

Finally, let's solve the last problem:

3. We are given the circumference of a sphere as 155mm, and we need to find the surface area of the sphere rounded to the nearest tenth.

The circumference of a sphere can be calculated using the formula:

Circumference = 2π(radius)

Given the circumference as 155mm, we can rearrange the formula to solve for the radius:

155 = 2π(radius)

radius ≈ 155 / (2π) ≈ 24.7mm

Using the formula for surface area (which is the same as in problem 2), we can calculate the surface area:

Surface Area = 4π(radius)^2

Surface Area = 4π(24.7)^2 ≈ 7647.4mm^2

Rounded to the nearest tenth, the surface area is 7647.4mm^2.

Therefore, the correct answer is 7,647.4mm^2.

I hope this helps! Let me know if you have any other questions.

Of course, I'd be happy to help you with these problems!

1) Let's tackle the first problem about the weight of the glass vase. We are given that the weight of a glass vase with certain dimensions is 0.12 lb. We then want to determine the weight of a similarly shaped vase with each dimension being 6 times as large.

To solve this, we can use the concept of volume and assuming that the density of the glass remains the same. Since the vases have a similar shape, the ratio of the volumes will be equal to the cube of the scaling factor (6). So, the volume of the new vase will be (6^3 = 216) times the volume of the original vase.

Let's denote the weight of the new vase as x lb. We can set up a proportion to solve for x:

0.12 lb / 1 = x lb / 216

Solving this proportion, we find:

x lb = (0.12 lb * 216) / 1
x lb = 25.92 lb

Therefore, the weight of the similarly shaped vase of the same glass is 25.92 lbs.

So, the correct answer to this problem is 25.92 lbs.

2) Moving on to the second problem about the surface area of a sphere, we are given the volume of the sphere as 5,000 pi m^3. We need to find the surface area to the nearest square meter.

To solve this, we need to use the formulas for volume and surface area of a sphere. The volume of a sphere is given by:

Volume = (4/3) * pi * r^3

Given that the volume is 5,000 pi m^3, we can set up the equation:

5,000 pi m^3 = (4/3) * pi * r^3

Simplifying and solving for r, we find:

r^3 = (3 * 5,000) / 4
r^3 = 3,750
r ≈ ∛3,750
r ≈ 14.48 m

Now, the surface area of a sphere is given by:

Surface Area = 4 * pi * r^2

Plugging in the value we found for r, we have:

Surface Area ≈ 4 * pi * (14.48 m)^2

Calculating this value, we get:

Surface Area ≈ 2,079.1 m^2

Thus, the correct answer to this problem is 2,079 m^2.

3) Lastly, we have the problem about the surface area of a sphere with a circumference of 155 mm. We want to find the surface area rounded to the nearest tenth.

To solve this, we need to use the formulas for circumference and surface area of a sphere. The circumference of a sphere is given by:

Circumference = 2 * pi * r

Given that the circumference is 155 mm, we can rearrange the formula to solve for r:

r = Circumference / (2 * pi)
r = 155 mm / (2 * pi)
r ≈ 24.65 mm

Now, the surface area of a sphere is given by:

Surface Area = 4 * pi * r^2

Plugging in the value we found for r, we have:

Surface Area ≈ 4 * pi * (24.65 mm)^2

Calculating this value, we get:

Surface Area ≈ 3,823.7 mm^2

Rounding this to the nearest tenth, the correct answer is 3,823.7 mm^2.

I hope this helps! Let me know if you have any further questions.