Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. 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.

Result

S =  597.66 cm²
V =  1373.89 cm³

Solution:

$r^2 = 60^2+34^2 = 4756 \ \\ r = 68.96 \ mm \ \\ S = 4\pi r^2 = 4 \pi \cdot 4756 = 597.66 \ cm^2$

$V = \dfrac43 \pi r^3 = \dfrac43 \pi\cdot 68.96^3 = 1373.89 \ cm^3$

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Spheres in sphere
   How many spheres with a radius of 15 cm can fits into the larger sphere with a radius of 150 cm?
2. Gasholder
   The gasholder has spherical shape with a diameter 20 m. How many m³ can hold in?
3. Hemispherical hollow
   The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
4. Fit ball
   What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
5. Cube corners
   From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
6. Truncated cone
   Calculate the height of the rotating truncated cone with volume V = 1115 cm³ and a base radii r₁ = 7.9 cm and r₂ = 9.7 cm.
7. Cross-sections of a cone
   Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
8. Cylinder surface, volume
   The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
9. Truncated cone
   A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume.
10. Cone area and side
    Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
11. Bottles of juice
    How many 2-liter bottles of juice need to buy if you want to transfer juice to 50 pitchers rotary cone shape with a diameter of 24 cm and base side length of 1.5 dm.
12. Frustum of a cone
    A reservoir contains 28.54 m³ of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
13. Surface area
    The volume of a cone is 1000 cm³ and the content area of the axis cut is 100 cm². Calculate the surface area of the cone.
14. Theorem prove
    We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
15. Tetrahedron
    Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
16. Bottles
    The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
17. Octahedron
    All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.