Right Circular Cone
Author: Lewis Prisco

Use this worksheet to practice finding the Volume and Surface Area of a Right Circular Cone. Adjust the height and radius using the labeled sliders.  Answer the questions below. The multi-colored switches can be used to check your work.

1.Find the volume and surface area for 5 different cones by randomly choosing different heights and radii.

2. Find the missing dimesion. Round to the nearest unit.
     a. Cone: volume 424 cubic meters, diameter 18 meters, height ___
     
     b. Cone: surface area 153.5 sq in, radius 4 in, slant height ___
    
3. Plants: A cone-shaped paper cup is 7 cm high with a diameter of 6 cm. If the ivy plant on Julia's desk needs 240mL of water, about how many paper cups of water will she use to water it? (1 mL = 1 cubic cm)

h

r

V=\frac{ 1 }{ 3 } πr²h

S.A.=πr(s.h.)+πr²

Tilavuuden kaava

Pinta-alan kaava

Pinta-ala

Tilavuus

korkeus = 8.4 (slider from 3 to 10, step 0.1)
säde = 4 (slider from 1 to 5, step 0.1)
s_1: sqrt(korkeus^(2) + säde^(2))
s_2: 3.141592653589793 säde s_1 + 3.141592653589793 säde^(2)
c: x^(2) / (2.5 säde)^(2) + y^(2) / (0.35 säde)^(2) = 1
A = (25, 10)
B = (25, 12.5)
P = (0, 0)
L: (-2.5 säde, 0)
R: (2.5 säde, 0)
C = Dilate(B, korkeus, A)
u = Vector(A, C)
E = Translate(P, u)
f = Arc(c, 3.141592653589793, 0)
Q, r_1, l, e = Polygon(L, E, R)
a = Segment(E, P)
b = Segment(P, R)
D = Midpoint(E, P)
F = Midpoint(P, R)
G = (16.90833333333334, 17.408333333333335)
H = (17.133333333333336, 14.108333333333334)
I = (17.433333333333337, 3.908333333333332)
J = (18.183333333333337, 7.208333333333332)
VolumeFormula = 0 (slider from 0 to 1, step 1)
VolumeSolution = 0 (slider from 0 to 1, step 1)
SurfaceAreaSolution = 0 (slider from 0 to 1, step 1)
SurfaceAreaFormula = 0 (slider from 0 to 1, step 1)
K = If(VolumeFormula ≟ 1, G)
M = If(VolumeSolution ≟ 1, H)
N = If(SurfaceAreaSolution ≟ 1, I)
O = If(SurfaceAreaFormula ≟ 1, J)
v_1: 1 / 3 * 3.141592653589793 säde^(2) korkeus
T5: v_1 + "=\frac{1}{3}" + "π" + säde + "^2 " + korkeus
S = Midpoint(E, R)
T6: "s.h.=" + s_1
T7: s_2 + "=" + "π" + säde + "(" + s_1 + ")+π" + säde + "^2"
T12: "korkeus=" + korkeus
T13: "säde=" + säde