Math help Surface Area and Volume of a Cylinder??

Question

Math help Surface Area and Volume of a Cylinder??

5. The glue stick has a diameter of 2.5 cm and a height of 10.5 cm. The glue inside has a diameter pf 2.5 cm and a height of 9.5 cm. What is the difference between the volume of the container and the volume of the glue?

6. The Da Silvas installed a cylindrical water heater with a radius of 30 cm and a height of 120 cm.

a) What is the surface area of the water heater?

b) What is the volume of the water heater?

7. a) Describe a method of measuring, with reasonable accuracy, the diameter and the height of the nickel. What are the diameter and the height?

b) What is the volume of a roll of 40 nickels?

c) What is the minimum surface area of the paper needed to roll a stack of nickels?

Please help even if you only know one or two answers thnx =) show the work

Answer 1

#5 - Volume of a cylinder is Pi x r squared (formula for area of a circle) x height.

Volume of Stick = Pi x 1.25 squared x 10.5 = 51.5 cm cubed
Volume of Glue = Pi x 1.25 squared x 9.5 = 46.6 cm cubed
Difference between stick and glue = 51.5 - 46.6 = 4.9 cm cubed

#6 a) A = Pi x r squared = 3.14 x (30cm)squared = 2826 cm cubed

#6 b) V = Area x height of cylinder = 2826 x 120 cm = 339120 cm cubed

#7 Use a ruler. You should be able to handle this, it's exactly like the first 2.

Answer 2

5. Volume of cylinder = area of circle X height of cylinder
Volume of glue stick = (pi X radius squared) X 10.5
(pi = 3.14159), (radius is half of diameter)
Volume of glue stick= (3.14159 X 1.25 squared) X 10.5

Volume of glue = area of circle X height of glue
= (3.14159 X 1.25 squared) X 9.5

Find these two volumes, and subtract. That is the difference.

6. Surface area is the areas of the outer surfaces all added together. The top and bottom circles, and the body of the cylinder, which would be a rectangle if you could open it up flat. The imaginary rectangle would have measurements of 120 and whatever the circumference of the circle is.
Circumference = pi X diameter
= 3.14159 X 60
Area of rectangle = circumference X height of cylinder
= 3.14159 X 60 X 120
area of one circle = pi X radius squared
= 3.14159 X 30 X 30
area of two circles = 2 X 3.14159 X 30 X 30
surface area of water heater = area of rectangle + area of two circles

Volume of water heater = area of circle X height
= (3.14159 X 30 X 30) X 120

Are you sure the measurements are given in centimeters? That is not a realistic size for a water heater. Anyway, the area answer would be in units squared, and the volume in units cubed.

7. I would use a micrometer to measure the nickel. If you don't have one, then measure it in millimeters. Find the diameter and height by measuring.
The volume of a roll of 40 nickels = area X height of nickel X 40
(the area is pi X radius squared, radius is half the diameter)

find the surface just like with the water heater problem.

Answer 3

You should be able to calculate the surface area of a cylinder by multiplying the diameter times the height. For question 5, for example, calculate the areas for both the glue stick and the glue inside by multiplying the diameter by the height for each and subtract the glue from the glue stick.

I am not going to give you the answers beyond that. You are plenty smart enough to do the math yourself and I would not be doing you a favor if I did that.

Good luck and knock 'em dead in your class.

Answer 4

entire floor area of cylinder = 2*pi*r*(r+h), the place r is radius and h is top. because of the fact r = h entire floor area of cylinder = 4*pi*r^2 ---------------(a million) quantity of cylinder = pi*r^2*h = pi*r^3 (because of the fact r = h) -------------- (2) Equate (a million) and (2) 4*pi*r^2 = pi*r^3 So r = 4 instruments and because r = h, the top is likewise 4 instruments. So the cylinder has the raduis besides as top of four instruments.