The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?

Result

p1 =  70.37 %
p2 =  55.556 %

Solution:

$r_{1}=1 \ \\ r_{2}=r_{1} - r_{1}/3=1 - 1/3 \doteq \dfrac{ 2 }{ 3 } \doteq 0.6667 \ \\ \ \\ V_{1}=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r_{1}^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 1^3 \doteq 4.1888 \ \\ V_{2}=\dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r_{2}^3=\dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 0.6667^3 \doteq 1.2411 \ \\ \ \\ p_{1}=100 \cdot \ \dfrac{ V_{1}-V_{2} }{ V_{1} }=100 \cdot \ \dfrac{ 4.1888-1.2411 }{ 4.1888 } \doteq \dfrac{ 1900 }{ 27 } \doteq 70.3704 \doteq 70.37 \%$
$S_{1}=4 \pi \cdot \ r_{1}^2=4 \cdot \ 3.1416 \cdot \ 1^2 \doteq 12.5664 \ \\ S_{2}=4 \pi \cdot \ r_{2}^2=4 \cdot \ 3.1416 \cdot \ 0.6667^2 \doteq 5.5851 \ \\ \ \\ p_{2}=100 \cdot \ \dfrac{ S_{1}-S_{2} }{ S_{1} }=100 \cdot \ \dfrac{ 12.5664-5.5851 }{ 12.5664 } \doteq \dfrac{ 500 }{ 9 } \doteq 55.5556 \doteq 55.556 \%$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

1. Spheres in sphere
How many spheres with a radius of 15 cm can fits into the larger sphere with a radius of 150 cm?
2. Inscribed sphere
How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
3. Earth's surface
The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?
4. Gasholder
The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
5. Hemispherical hollow
The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
6. Red diplomas
He numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase?
7. Researchers
Researchers ask 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the families
8. Winery
The wine processing plant sold 8/15 of its total wine production to the domestic market, 2/7 to the foreign the rest of the wine. How many percents are still in stock?
Iva added one liter of 100% fruit juice to 3 liters of water. She left two liters of it for Alice and Beata. She added two more liters of water to the remain two liters of lemonade and offered it to other friends. a. What percentage of juice did Alena an
10. Summerjob
The temporary workers planted new trees. Of the total number of 500 seedlings, they managed to plant 426. How many percents did they meet the daily planting limit?
11. Percentage 10
52 shorts and missed 13. Calculate percentage
12. Profit gain
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:
13. Vinegar mixing
We mix 70g water and 50g 8% vinegar. How many percents of the solution of vinegar we produce?
14. Mixed with percentages
Calculate 33 1/3% of 570.
15. Cake ingredients
The yeast cake contains milk, yeast, sugar, and flour in a ratio of 20: 4: 1: 15. What percentage of flour is in yeast?
16. Speedometer
The speedometer of a car reads 66 km/h. It's accurate to within 4.1% What is the maximum possible error?
17. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?