The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm². Calculate correct to 3 significant figures:

*Base Radius
*Height
*Volume of the cone

Result

r =  3.501 cm
h =  9.899 cm
V =  127.059 cm³

Solution:

$s=10.5 \ \text{cm} \ \\ S_{1}=115.5 \ \text{cm}^2 \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s \ \\ \ \\ r=\dfrac{ S_{1} }{ \pi \cdot \ s }=\dfrac{ 115.5 }{ 3.1416 \cdot \ 10.5 } \doteq 3.5014 \doteq 3.501 \ \text{cm}$

$s^2=h^2 + r^2 \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 10.5^2-3.5014^2 } \doteq 9.8991 \doteq 9.899 \ \text{cm}$

$S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 3.5014^2 \doteq 38.5065 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{2} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 38.5065 \cdot \ 9.8991 \doteq 127.0586 \doteq 127.059 \ \text{cm}^3$

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. 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.
2. 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.
3. Cut and cone
   Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
4. Slant height
   The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
5. Pile of sand
   A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
6. Cone container
   Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
7. 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.
8. Truncated cone 5
   The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
9. Sphere cuts
   At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
10. Equation of circle
    find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
11. Tetrahedron
    Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
12. 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?
13. Holidays - on pool
    Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
14. Circle annulus
    There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
15. Chord
    It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
16. Circle's chords
    In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
17. RT and circles
    Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.