Geometry help?

Question

A spherical scoop of ice cream with diameter 6 cm is placed in an ice-cream cone with diameter 5 cm and height 10 cm. Is the cone big enough to hold all the ice cream if it melted?

How would you solve for the answer? Step-by-step.

Answer 1

Volume of the cone = 1/3 * pi * r^2 * h
= 1/3 * pi * 2.5^2 * 10 = 65.45 cc

Volume of the sphere = 4/3 * pi * r^3
= 4/3 * pi * 3^3 = 113.10 cc

No, the cone would not be big enough to fit the melted ice cream.

Answer 2

First find the volume of the ice cream then find the volume of the cone. This is because if the icecream melts you need to see if all of it will fit into the cone.

Volume of Sphere: (4/3)*pi*r^3
Volume of Cone: 1/3(pi*r^2)(height)

Volume of Icecream is then:
r = 6/2 =3
(4/3)*pi*(3^3) = 113.1cm^3

Volume of the Cone is then:
r = 5/2
h = 10
1/3(pi*(5/2)^2)*10 = 65.4cm^3

Therefore since the volume of the icecream is larger than the volume of the cone, the cone is not big enough to hold all of the ice cream.

Answer 3

volume of icecream = volume of scoop = 4/3r3
whr r is radius of spherical scoop i.e 3 cm
therefore volume of icecream = 4/3 II (3)3
= 36 (3.14) cubic cms
= 113.04 cubic cms
Volume of icecream cone = 1/3 II r2 h
where r is radius of cone
h is height of cone
therefore volume of cone = 1/3 (3.14) (2.5)2 (10)
= 1/3 (31.4) 6.25
= 654. 17 cubic cms

voulme of icecream > volume of cone
therefore cone is not big enough to hold all ice cream if melted

Answer 4

well basically, they're asking you if the cone's volume is bigger or equal to the volume of the sphere. so you need to find both volumes

for the sphere's volume, you have the radius (3cm).
sphere volume is (4/3) * pi * r^3 = 113.097 cm^3

cone volume is (1/3) * pi * r^2 * h
you have the height (10cm) and radius (2.5cm) so the volume is: 65.4498.

so the cone is not big enough. Hope that helped.

Answer 5

V (sphere) = (4/3)π x 3³ cm³ = 36π cm³
V(cone) = (1/3).π x 2.5² x 10 = 21π cm³
Cone is not big enough.

Answer 6

Cone:
V=1/3pi(r^2)h
1/3 x 3.14 x 2.5^2 x 10
V=64.76

Scoop:
V=4pi(r^2)
4 x 3.14 x 3^2
V=113.04

no