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:
- Mr. Lee
Mr. Lee has a rope. The total length of the rope is 5 meters. He cuts off 350 centimeters of rope to use in his garden and another 75 centimeters to hang a bird feeder. What is the length of the rope he has left in centimeters? - Slow traveler
A little mouse travels 3.6 km in 1 hour. What is its speed in m/s? - Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC. - Maria 6
Maria drank 3 liters of water last week. Her friend drank twice as much water as Maria. How many milliliters of water did they both drink? - Saw a board
A board of 16 3-fourths inches is cut from a board that is 3 feet long. If the width of the saw cut is one-eighth inch, what is the length of the remaining piece? - Kangaroo 82979
A kangaroo can move at a speed of 65 km/h. How many minutes will it take to move at this speed to a place 6500 m away? - Write a blog
You spend 2 1/2 hours online. You spend 1/5 of that time writing a blog. How long do you spend writing that blog? - Hoverboard
Adam lives in Podhradí, and his friend Marcel lives in Lhota. Lhota is 6 km from Podhradí. Adam travels the same distance on a hoverboard in 20 minutes as Marcel does in 25 minutes. They leave home simultaneously, drive towards each other, and meet in pre - X-triangle
Find the length of the x segment in the given triangle drawings. - Vegetable storage
To help vegetables stay fresh longer, Liam's family maintains storage near their home. The total volume of the root cellar is 737 cubic feet (ft³). Use the fact that 1 foot is approximately equal to 0.3048 m to convert this volume to m³. Round your answer - Mast angles and height
Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast. - Speed problem
Convert 540 meters/minute to Kilometer/hour. - Using 4
Using the law of cosines, find the measurement of leg b if the givens are B=20°, a=10, and c=15. - Yd2 to ft2 unit conversion
If a room requires 25.4 square yards of carpeting, what is the area of the floor in units of ft2? (3 ft. = 1 yd.) - A triangular
A triangular frame has sides that measure 15’-7",20’-4", and 26’-2". What is the total length of the three sides? - A road
A road on a map measures 8cm long. The scale of the map is 25000. Calculate the actual length of the road - Cone-shaped 82466
The cone-shaped glass has a volume of 2.5 dl and a diameter of 13 cm. How much cocktail is left in the glass if the level only reaches half the height of the glass?