Find the Lateral Area, Surface Area, and Volume of a cone?

Question

with radius 9 cm and slant height 15 cm

Answer 1

The first guy is unfortunately wrong. Although he's using the correct formula for volume, the height given in the question is "slant height" which is different from the actual height of the cone. The "slant height" is actually the hypotenuse of a triangle with the short side being the radius of 9cm and the long side computed with the pythagoreum theorum (the square of the hypotenuese = the sum of the squares of the other two sides. So you find out the actual height by doing this: 15 squared = 9 squared + x squared. So the actual height of the cone is 12 instead of 15 like the first guy posted incorrectly. Use the same formulas, just remember that the height of the cone is 12, and you use the pythagoreum theorum to find it. (Basic Geometry)

Answer 2

These people are forgetting that the slant height is not the height of the cone. You already have the slant height, so you don't need to calculate anything to find it: s = √( r² + h²) = 15 cm. From that, you can calculate the height of the cone:

s² - r² = h²
(15)² - (9)² = h²
225 - 81 = h²
144 = h²
12 cm = h

Now find the volume of the cone:

V = 1/3 π r² h (where h is the height of the cone, not the slant height)
V = 1/3 π (81cm²)(12 cm)
V = 324π cm³
V ~ 1017.88 cm³

Lateral Area = π r s
= π (9 cm)(15 cm)
= 135 π cm²
~ 424.12 cm²

Surface Area = Lateral Area + Area of Base
S. A. = π r s + π r² = π r (s + r)
= π (9 cm)[15 cm + 9 cm]
= 216 π cm²
~ 678.58 cm²

Answer 3

Volume = 1/3 pi r^2 h

V = 1/3 pi (9^2)(15)
V = 405 pi cubic cm

Lateral = pi* r *sqrt(r ² + h ²)
L = pi(9)sqrt(81+225)
L = 9 pi sqrt306 square cm

The surface area is the sides plus the circle(area circle pi r^2)
Surfacre area = Lateral + pi r^2
S = 9 pi sqrt306 + pi (9^2)
S = (81 + 9 sqrt306) pi

{I do not have calculator, you will have to do the calcs... sorry)

Answer 4

to detect the lateral component of a cone, locate one-0.5 the made from the circumference and the slant top, or L.A. = a million over 2(2?r)L. word this formulation simplifies to L.A. = ?rL floor section = ?(r^2) + ?rL quantity = (a million/3)?(r^2)h r=5 L=13 via Pythagorean Theorem: h=sqrt[(13^2)-(5^2)] h=sqrt[(169)-(25)] h=sqrt[one hundred forty four] h=[12] so which you have a cone: r=5cm L=13cm h=12cm Lateral section: L.A. = ?rL L.A. = ?(5)(13) L.A. = 65? floor section: S.A. = ?(r^2) + ?rL S.A. = ?(5^2) + ?(5)(13) S.A. = ?(25) + ?(sixty 5) S.A. = 90? quantity: V = (a million/3)?(r^2)h V = (a million/3)?(5^2)*(12) V = (a million/3)?(25)(12) V = (25)?(4) V = 100?

Answer 5

The lateral area= 423.9 cm^2
The surface area= 678.24 cm^2
The volume= 90 cm

Answer 6

Use the formulas for a cone:
V = (1/3) π r ² h
Lateral area = π r √(r ² + h ²)
Surface area = [lateral area] + [π r ²]