911782
17.03.2021 •
Mathematics
(a) Show that the volume of a metal sphere of radius 15 cm is 14140 cm”, correct to 4 significant
figures
[The volume, V. of a sphere with radius r' is V=
V=tr'
(b) (i)
The sphere is placed inside an empty cylindrical tank of radius 25 cm and height 60 cm.
The tank is filled with water.
25 cm
NOT TO
SCALE
60 cm
Calculate the volume of water needed to fill the tank
Solved
Show answers
More tips
- F Food and Cooking Do Aphrodisiacs Really Work? Separating Fact from Fiction...
- C Computers and Internet Log-in: what is it and why do you need it?...
- S Style and Beauty Secrets of Tying a Pareo: 5 Ways...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- C Computers and Internet How to Learn to Type Fast?...
Answers on questions: Mathematics
- M Mathematics Find the equation, in slope-intercept form, of the line through the pair of points (2,0) (3,4)...
- M Mathematics Find the difference between 1.42m and 29cm express the answer in cm...
- C Computers and Technology Which sentence indicates that Jeff is mentioning the visual synopsis in his proposal while planning a media project? (Choose only one number that is correct) An the proposal,...
- M Mathematics -29=9-6k-2k-14 help lauvs...
- H History Why do you think the War in the East went so poorly for the Union? (drop your opinions :) )...
Ответ:
a) The volume of the sphere is approximately 14,137.16694 which is 14,140 cm³ correct to 4 significant figures
b) The volume of water required to fill the tank is approximately 103,670 cm³
Step-by-step explanation:
a) In the question, the radius of the sphere, r = 15 cm
The formula for the volume, 'V', of a sphere is given as follows;
Where;
r = The radius of the the sphere
V = The volume of the sphere
Plugging in the value for the radius, 'r', of the sphere, in the equation for, 'V', we get;
Therefore;
The volume of the sphere to 4 significant figures is V ≈ 14,140 cm³
b) The parameters of the cylindrical tank are;
The height of the cylindrical tank, h = 60 cm
The radius of the cylindrical tank, r = 25 cm
The volume of a cylinder, V = π·r²·h
∴ The volume of the cylindrical tank without water, '', is given as follows;
= π × (25 cm)² × 60 cm ≈ 117809.72451 cm³
The volume of water, , required to fill the tank with the sphere of volume 'V' placed inside is given as follows
= V +
∴ = - V
From which we get;
≈ 117809.72451 cm³ - 14,140 cm³ = 103,669.72451 cm³ ≈ 103,670 cm³
The volume of water required to fill the tank, ≈ 103,670 cm³.
Ответ:
If using simple interest, the formula is:
= Amount * ( 1 + rate * time)
= 20,000 * ( 1 + 4% * 5)
= $24,000
Interest = Balance after 5 years - Investment
= 24,000 - 20,000
= $4,000
Using Compound Interest:
= Amount * ( 1 + rate)^time
= 20,000 * ( 1 + 4%)⁵
= $24,333.06
Interest = 24,333.06 - 20,000
= $4,333.06