Question

1. Use Euler’s formula to find the missing number.

Answer 1

Answer:

Faces=11 faces

surface area=1112 square meters

slant height=4.5 cm

Step-by-step explanation:

Part 1: Given that

Vertices=15

Edges=24

we have to find the number of faces by using Euler's formula    

Euler's formula shows the relation between vertices, edges and face for convex polyhedron.

It states that the number of vertices and faces is exactly 2 more than no. of edges i.e

V-E+F=2

⇒ 15-24+F=2

⇒ F=2+24-15=11

Hence, number of faces are 11

Part 2: Given the height and diameter of cone

Height=43 m

Diameter=14 m

∴ $Radius=\frac{1}{2}\times 14=7m$

$\text{surface area of cone=}\pi r(r+\sqrt{h^2+r^2})$

$=\frac{22}{7}\times 7(7+\sqrt{7^2+43^2})=1112.01\sim 1112 m^2$

Part 3: Given

$\text{The lateral area of a cone is }612 cm^2$

Radius=43 cm

$Area=\pi rl=\frac{22}{7}\times 43\times l$

$612= \frac{22}{7}\times 43\times l$

$\frac{612 \times 7}{22\times 43}=l$

$l=4.5285\sim 4.5 cm$

Answer 2

V + f = a + 2
15 + f = 24 + 2

f = 26 - 15
f = 11 (11 faces)

height = 43 m
d = 14m
r = 7 m
A = π.r.g
g² = r²+h²
g² = 7²+43²
g² = 1898
g = \/1898
g ~ 43,56 m
A = π.r.g
A = π.7.43,56
A = 304,92 π
A = 304,92*3,14
A = 957,45 m² (área lateral)