The base 2

The base diameter of a right cone is 16cm and it's slant height is 12cm.
A. ) Find the perpendicular height of the cone to 1 decimal place.
B. ) Find the volume of the cone, convert to 3 significant figure. Take pie =3.14

Correct answer:

h =  8.9 cm
V =  599.451 cm³

Step-by-step explanation:

$$\begin{gathered} D=16\text{ cm } \\ s=12\text{ cm } \\ r=D\mathrm{/}2=16\mathrm{/}2=8\text{ cm } \\ {s}^2=r^2+h^2 \\ h=\sqrt{s^2-r^2}=\sqrt{12^2-8^2}=4\sqrt{5}=8.9\text{ cm} \end{gathered}$$

$V={\displaystyle \frac{1}{3}}\cdot \pi \cdot r^2\cdot h={\displaystyle \frac{1}{3}}\cdot 3.1416\cdot 8^2\cdot 8.9443=599.451{\text{cm}}^3$

Try another example

Related math problems and questions:

• Slant height
  The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
• 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
• Cone - from volume surface area
  The volume of the rotating cone is 1,018.87 dm³, and its height is 120 cm. What is the surface area of the cone?
• Body diagonal
  Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
• Isosceles + prism
  Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm length of 3.7 cm
• 3sides prism
  The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
• Rotating cone
  Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm.
• The conical
  The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
• Quadrilateral pyramid,
  A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
• 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 sandpile is 31 feet. Find the volume of the pile of sand.
• Axial section of the cone
  The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
• Triangular pyramid
  It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is it content (surface area)?
• Cutting cone
  A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
• Base of prism
  The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm².
• Cone and the ratio
  The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm?
• Rectangular triangle PQR
  In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal