What is the surface area of the geometric solid produced by the 30-60-90 triangle below when it is rotated 360 degrees about the axis RD? Support your answer.

The surface area of the cone is 9.42cm²

Explanation:

When a triangle with the interior angle as 30°-60°-90° is rotated then a cone is formed.

So, 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 = lateral height of the cone

tan (30°) =

So,

BC = 1

AB = √3

AC = ?

(AC)² = (BC)² + (AB)²

(AC)² = (1)² + (√3)²

AC = 2

Lateral height, h = 2cm

Radius = BC = 1cm

Thus,

surface area of the cone = πr ² + πrl

Therefore, surface area of the cone is 9.42cm²

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x