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:
- algebra
- expression of a variable from the formula
- intersection of sets
- solid geometry
- cone
- sphere
- surface area
- planimetrics
- circle
- area of a shape
- triangle
- basic functions
- ratio
- goniometry and trigonometry
- tangent
- arctangent
Units of physical quantities:
Grade of the word problem:
Related math problems and questions:
- Sin cos tan
If cos y = 0.8, 0° ≤ y ≤ 90°, find the value of (4 tan y) / (cos y-sin y) - ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - A chord
In a circle radius of 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the cord at the center of the circle Hence find the length of the minor arc cut off by the chord. - Angle of the sector
Find the angle of the sector of a circle radius of 20 units where the area is equal to the lateral area of a cone with a radius of 8 units.
- Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - Corresponding 59063
Calculate the radius and area of the circular segment if the center angle = 106° and the length of the corresponding circular arc is l = 52 cm. - Quadrilateral in circle
A quadrilateral is inscribed in the circle. Its vertices divide the circle in a ratio of 1:2:3:4. Find the sizes of its interior angles. - Convex angle
There is a circle k (S; r), and a point A, which lies on this circle. There is also a point B on the circumference, for which it is true that in one direction, it is five times further from point A than in the opposite direction (around the circumference - Circle segment
A quarter circle with a radius of 4 has the same area as a circle segment with a radius of 3. What is the magnitude of the center angle of the circle segment?
- Two waves
Two waves are out of phase by 26°. If the period of the waves is 6 seconds, what is the time difference between the waves? Give your answer in seconds to 2 decimal places. - Angle ASB
On a circle with a radius of 10 cm and with a center S, the points A, B, and C are given so that the central angle ASB is 60 degrees and the central angle ASC is 90 degrees. Find the length of the circular arc and the amount of AB and AC offsets. - Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles? - Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°. - Minute hand
What is the distance the clock's minute hand travels in 12 minutes if the clock's diameter is 30 cm and the hand extends to a distance of 2 cm from the edge of the clock?
- Surveyors
Surveyors mark 4 points on the globe's surface so their distances are the same. What is their distance from each other? - Carousel for children
There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2m? - Seats on carousel
There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5m?