Right Circular Cone
Author: L. Prisco & R. Valcin

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. Click on the check boxes to find helpful hint and verify your answers.

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

2. Find the missing dimensions below. Round to the nearest unit.
     a. Cone: volume is 424 cubic meters, diameter is 18 meters, height ___
     
     b. Cone: surface area is 153.5 square inches, radius is 4 inches, 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)

V=\frac{ 1 }{ 3 } πR²H=\frac{π*R*R*H }{3} 

נוסחה לנפח חרוט

חישוב

חרוט

R  

H 

הצג גליל החוסם את החרוט

נוסחה לשטח פנים של חרוט

P=πR² + πRL

L 

חישוב

H = 10 (slider from 0 to 10, step 0.1)
R = 5 (slider from 1 to 5, step 0.1)
s_1: sqrt(H^(2.0) + R^(2.0))
s_2: 3.14 * R * s_1 + 3.14 * R^(2.0)
c: x^(2.0) / (2.5 * R)^(2.0) + y^(2.0) / (0.35 * R)^(2.0) = 1.0
A = (25, 10)
B = (25, 12.5)
P = (0, 0)
L: (-1.0 * 2.5 * R, 0.0)
R_1: (2.5 * R, 0.0)
C = Dilate(B, H, A)
u = Vector(A, C)
E = Translate(P, u)
f = Arc(c, 3.141592653589793, 0.0)
Q, r_1, l, e = Polygon(L, E, R_1)
a = Segment(E, P)
b = Segment(P, R_1)
D = Midpoint(E, P)
v_1: 3.14 * R * R * H / 3.0
d = false
h_1 = false
v_2: 3.14 * R * R * H
a_1: 3.14 * R * s_1
a_2: 3.14 * R * R
K = Midpoint(a)
g = OrthogonalLine(R_1, e)
h = OrthogonalLine(L, e)
c' = Translate(c, u)
F = Intersect(c', g, 1.0)
G = Intersect(c', h, 1.0)
j = Segment(G, L)
k = Segment(F, R_1)
m = false
i = false
T5: "V= " + "\frac{1}{3}" + "*" + "3.14" + "*" + R + "*" + R + "*" + H + " =  " + "\frac{" + v_2 + " }{ 3}" + " = " + v_1 + "  קמס  "
text4: "P= 3.14 *" + R + "*" + R + "+ 3.14*" + R + "*" + l + " = " + s_2 + " סמר"
n = false