yvettebook
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Can someone please help me in detail if two spherical pieces of cookie dough have radii of 3cm and 5cm. The pieces are combined to form one large spherical piece of dough. What is the approx radius of the new sphere of dough?




Ratio of two volume cylinders (Geometry)

If two similar cylinders have heights of 75cm and 25cm. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder? Can someone please explain in detail. Thank you!

Sagot :

Trim
The ratio of the lengths is 75 : 25 or 3 : 1 

The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2
(In working out the area the radius is squared)

The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3
(In working out the volume the radius is cubed)

Hopefully this explains it
Volume of a sphere:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Combining dough is like combining volume. So we get
[tex]V_3=\frac{4}{3}\pi r_3^3=\frac{4}{3}\pi r_1^3 + \frac{4}{3}\pi r_2^3 = \frac{4}{3}\pi (r_1^3+r_2^3)[/tex]
Where [tex]V_3 [/tex] is the combined volume of dough of radii [tex]r_1[/tex] and [tex]r_2[/tex]
The new radius is therefore
[tex]r_3^3=r_1^3+r_2^3[/tex]
Substituting values we get
[tex]r_3^3=3^3+5^3=27+125=152[/tex]
[tex]r_3=\sqrt[3] 152 \approx 5.34[/tex]

So the new dough is 5.34 cm, just a bit larger.

Cylinders:
[tex]V=\pi r^2 h[/tex]
So volume is directly proportional to height, if radius is constant. So ratios stay the same. 75/25=3 and the volume is also 3 times larger (ratio 3:1).
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.