# 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:

*Height
*Volume of the cone

Result

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

#### Solution:

$s=10.5 \ \text{cm} \ \\ S_{1}=115.5 \ \text{cm}^2 \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s \ \\ \ \\ r=\dfrac{ S_{1} }{ \pi \cdot \ s }=\dfrac{ 115.5 }{ 3.1416 \cdot \ 10.5 } \doteq 3.5014 \doteq 3.501 \ \text{cm}$
$s^2=h^2 + r^2 \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 10.5^2-3.5014^2 } \doteq 9.8991 \doteq 9.899 \ \text{cm}$
$S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 3.5014^2 \doteq 38.5065 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{2} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 38.5065 \cdot \ 9.8991 \doteq 127.0586 \doteq 127.059 \ \text{cm}^3$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.

## 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. Common chord
Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
10. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
11. 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?
12. 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?
13. 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?
14. 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.
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. RT and circles
Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
17. Chord - TS v2
The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?