Surface area ??

Question

9. What is the surface area if a cylinder which has a base radius of 7.5 m and a height of 4.9 m?

10. What is the surface area of a cone which has a base radius of 8.7 cm and a slant height of 9 cm?

11. What is the surface area of a sphere which has a radius of 9 dm?

12. A streamroller is flattening a new section of pavement. The diameter of the roller is 1.8 m and its face is 2.5 m wide. The section of road to be rolled is 0.9 km long.

a) How many times does the drum revolve in travelling 0.9 km?

b) What is the area flattened by the roller in travelling this distance?

Please help even if you only know one or two questions and show your work ?

Answer 1

9. View the cylinder as 3 major parts: the top circle, the bottom circle, and the long part.

Area of each circle = pi*radius^2 = pi*(7.5^2) = 56.25*pi = 176.79

Circumference of circle = 2*pi*radius = 47.14

Then area of long part = 4.9*47.14= 231

So total surface area = 176.79+176.79+231 = 584.58 metres squared.



10. Too long to explain. Use the link below and you should be fine.



11. Surface Area of a sphere = 4*pi*radius squared

And radius = diameter/2 = 9/2 = 4.5

= 4*pi*(4.5^2)

= 254.57 metres squared



12. First observe that 0.9km = 900m

Circumference of roller = pi*diameter = 2*1.8 = 3.6m

a) Number of revolutions = 900/3.6=250 revolutions



b) Area flattened = 900*2.5=2250 metres squared

Answer 2

9

2*pi*R*(H+R)=the surface area of a cylinder including The sides, the top and the bottom.

2*pi*R*R is the surface area of a cylinder without including a top and bottom.



10.

SH*pi*BR is the area of a cone

It can be developed by recognizing that if the cone were sliced from the point to the edge and flattened the cone it would be in the shape of a circle with a wedge cut out of it.

The radius of the circle would be the Slant Height. The ratio of the circumference of the base of the cone to the circle is the percentage of the circle that makes up the surface of the cone. The ratio of the circumferences is equal to the ratio of the radii.

BR/SH*pi*SH*SH=BR*pi*SH

11

4/3*pi*R*R*R

12.a

distance/circumference=number of times the roller turns

circumference=pi*Diameter

12.b

the area flattened equals the width times the distance.

Answer 3

portion of somewhat (sector)= the perspective of the international/ 360 x 2pie radius the comprehensive floor are of a cone is= pie x radius x length + pie x radius(sq.) The curved floor portion of a cone= pie x length x radius Curved floor portion of a cylinder= 2 x pie x radius x height entire floor portion of a cylinder= 2 x pie x radius x height + 2 x pie x radius (sq.) there is no formulation for the exterior are of a pyramid. in elementary terms the quantity os a pyramid is calculated.

Answer 4

09. 584.04

10. 2080.217007627

11. 1017.36dm^2

12. a) .5 times

b) 1.25m^2