Answer:
The volume of the solid is 19. unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
Where;
a = 1, and b = 2, we have;
g(x) = 1
The volume of the solid, V = unit³ = 19.
unit³
Answer:
area: 454.2 sq.cm
perimeter: 77.7 cm
Step-by-step explanation:
to find area, find the area of all the separate shapes and add them together:
semi-circle:
radius is 12 cm
area = = 226.2 sq.cm
separate the trapezoid into two right triangles and a rectangle.
area for triangles:
(5)(12) = 30
30 x 2 = 60 sq.cm (since there are two triangles)
area for rectangle:
12 x 14 = 168 sq.cm
area of whole shape: 226.2 + 60 + 168 = 454.2 sq.cm
for perimeter, just add the length of the exterior sides together.
we have some unknown sides, such as the semicircle and the sides of the trapezoid
we can find the hypotenuse of the triangles we used earlier to find the sides of the trapezoid with pythagorean theorem
c = 13 cm
to find the outside perimeter of the semi-circle, solve as if you were finding the circumference of a normal circle and divide it in half
= 37.7 cm
now add it all up:
14 + 13 + 13 +37.7 = 77.7