In the cone, the height is 15cm. and the generatrix is inclined to the base at an angle of 45 degrees.

| May 23, 2021 | education

In the cone, the height is 15cm. and the generatrix is inclined to the base at an angle of 45 degrees. Find the side of the cone.

In the drawing, a right-angled triangle ABC, in which AB is the height of the cone H (equal to 15 cm by condition), BC is the radius of the cone R.

The angles of a triangle add up to 180 degrees. Angle B is a straight line (90 degrees), angle C = 45 degrees (by condition), which means angle A = 180 – 90 – 45 = 45 (degrees). It follows that the ABC triangle is isosceles (since the angles at the base are equal).

Hence, AB = BC. That is, BC = R cone = 15 cm.

Next, we apply the formula for calculating the area of ​​the lateral surface of the cone, which is also located at the link (see above). We substitute the data known to us (R and H) into it. Find the area you are looking for.

Answer: 225 π√2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.