Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle. Find the size of the angle for the base of this triangle.
Correct answer:

Tips for related online calculators
Check out our ratio calculator.
Do you want to convert area units?
Calculation of an isosceles triangle.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
Do you want to convert area units?
Calculation of an isosceles triangle.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
You need to know the following knowledge to solve this word math problem:
algebrasolid geometryplanimetricsbasic operations and conceptsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem
Related math problems and questions:
- Conditions 7186
Given an isosceles right triangle ABS with base AB. On a circle centered at point S and passing through points A and B, point C lies such that triangle ABC is isosceles. Determine how many points C satisfy the given conditions and construct all such point
- The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (The cone side is the segment joining the vertex cone with any point of the base circle. All sides
- The chord
A chord passing through its center is the side of the triangle inscribed in a circle. What size are a triangle's internal angles if one is 40°?
- Sphere
Intersect between the plane and a sphere is a circle with a radius of 60 mm. The cone, whose base is this circle and whose apex is at the center of the sphere, has a height of 34 mm. Calculate the surface area and volume of a sphere.
- A cone 4
A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts.
- Determine the surface area
Find the surface area of a cone of height 30 cm whose side makes an angle of 60° with the base plane.
- Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?