A right open bottom cone with a capacity of 250 mL, what are the missing measurement facts?

Question

A right open bottom cone with a capacity of 250 mL, the radius is 4 cm, what is the volume and the surface area? 

Answer 1

A right open bottom cone with a capacity of 250 mL, the radius is 4 cm, what is the volume and the surface area?

 

1 cc = 1 mL

 

V = 250 cm^3 = (1/3) B h

B = pi r^2 cm^2

r = 4 cm

 

250 cm^3 = (1/3) pi 4^2 h

 

h = 750/(16 pi)

 

S.A. = pi h^2 * 2 pi 4 / (2 pi h)

 

S.A. = pi h^2 * 4 / h

 

S.A. = 4 pi 750/(16 pi)

 

S.A. = 750/4 =187.5 cm^2

Answer 2

Hi, Maddi.

 

The capacity IS the volume, but since the radius is measured in cm, we need to covert 250 mL to cubic centimeters (cc, or cm³).

 

1 mL = 1 cm³

so, 250 mL = 250 cm³

The volume of the cone is 250 cm³.

 

The formula for volume of a cone is   V = 1/3 πr²h

250 = 1/3·3.14159265·16·h

h = 14.9208 

The height of the cone is 14.9208 cm.

 

To find the surface area of the cone, we also have to know the slant height (s). The radius, the height of the cone and the slant height form a right triangle, so we can use the Pythagorean Theorem to find s.

 

s² = (14.9208)² + 4²

s = √238.6295544

s = 15.4476 

The slant height is 15.4476 cm.

 

The formula for area of a cone is πrs. (Since it is an open-bottom cone, we don't need to find the area of the circle.)

 

SA = 3.14159265·4·15.4476

SA = 194.1202665

The surface area is approx. 194.1203 cm².

 

Hope this helps!

Kathye P.