5. What is the volume of the geometric solid produced by the triangle below when it is
1 answer:
The diagram of the triangle is missing, so i have attached it.
Answer:
Surface area = 9.425 sq.units
Step-by-step explanation:
When a triangle having an interior angle as 30°, 60° or 90° is rotated, then a cone is formed.
Thus, we need to find the surface area of the cone.
Surface area of a cone is πr ² + πrL
where;
r = radius of the cone
L = slant height of the cone
I have attached the cone formed as the second image.
Looking at the image of the cone, we need to find the radius and slant height.
From the triangle image, we can use trigonometric ratios;
tan 30 = BC/AB
In surd form, BC/AB = 1/√3
Thus, BC is equivalent to 1 and AB equivalent to √3
Using Pythagoras theorem, we can find AC.
(AC)² = (AB)² + (BC)²
AC = √[(AB)² + (BC)²]
AC =√[(√3)² + (1)²]
AC = √[3 + 1]
AC = √4
AC = 2
So, radius, r corresponds to BC = 1
And slant height L corresponds to AC = 2.
Thus,r = 1 and L = 2
So,
Surface area of cone = π(1)² + π(1)(2) = π + 2π = 9.425 sq.units
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