Question

1. Use Euler’s formula to find the missing number.
Vertices: 15
Edges: 24
Faces: ?
• 9
• 10
• 11
• 12
7. What is the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters? Round the answer to the nearest square meter.
• 1,100 square meters
• 1,112 square meters
• 2,507 square meters
• 2,605 square meters
8. The lateral area of a cone is 612 cm2. The radius is 43 cm. What is the slant height to the nearest tenth of a centimeter?
• 4.5 cm
• 7.1 cm
• 9.1 cm
• 14.2 cm

Answer 1

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)

Answer 2

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

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

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

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

$l=4.5285\sim 4.5 cm$