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Geometry MATH PROBLEMS?
write the vector 11<30 degrees in a rectangular form
is this the answer 11cos30=9.52
11 sin30=5.5
sqaureroot 9.52^2+5.5^2=10.99
The circumference of the base of a right circular cone is 40m and the slant height is 38m. what is the area of the lateral surface?
is this the answer 38m/2=19m
1 Answer
- Anonymous1 decade agoFavorite Answer
In rectangular form (components) you would write the vector:
(11 cos(30), 11 sin(30))
and then substitute the values for the sin and cos.
The exact value (rather than a rounded one) is:
(11 sqrt(3) / 2, 11 / 2).
Alternatively, using i / j notation, you could write:
[ 11 sqrt(3) / 2 ] i + [ 11 / 2 ] j.
By adding the squares of the components and taking the square root, all you have done is get back to the original magnitude (11) with a rounding error. You don't need that in the answer. The components alone are sufficient.
The lateral surface area of a cone is:
pi r s
where r is the radius of the base and s is the slant height.
As the circumference is 40m, the radius is (40 / 2pi) metres, giving lateral surface area:
pi (40 / 2pi) 38
= 20 * 38
= 760 m^2.
The area cannot be expressed in metres -- it has to be square units.