Surface area of pyramids and cones worksheet answers pdf

Problem 1 :

Table of Contents Show

What is the surface area of the cone?
How to Find the slant height of a pyramid?
What is the surface area of a regular pyramid?

Find the surface area of the regular pyramid shown below.

Problem 2 :

The lateral faces of the Pyramid Arena in Memphis, Tennessee, are covered with steel panels. Use the diagram of the arena shown below to find the area of each lateral face of this regular pyramid.

Problem 3 :

Find the surface area of the regular pyramid shown below.

Problem 4 :

Find the surface area of the right cone shown below.

Problem 5 :

The surface area of a right cone is 30π square inches and the slant height is 7 inches. Find the radius of the base of the cone.

Answers

1. Answer :

The base is a square.

Use the formula for the area of a square to find the area of the base,

B = side ⋅ side

B = 2 ⋅ 2

B = 4 cm2

The perimeter of the base is

P = 4 ⋅ side

P = 4 ⋅ 2

P = 8 cm

The slant height is

l = √2 cm

Formula surface area of a right pyramid is

S = B + 1/2 ⋅ Pl

Substitute 4 for the area of the base B, 8 for P and √2 for l.

S = 4 + 1/2 ⋅ (8)(√2)

Simplify.

S = 4 + 4√2

Use calculator.

S ≈ 9.7

So, the surface area of the regular pyramid is about 9.7 square cm.

2. Answer :

To find the slant height of the pyramid, use the Pythagorean Theorem in the right triangle triangle shown below.

(Slant height)2 = h2 + (1/2 ⋅ s)2

Substitute.

(Slant height)2 = 3212 + 1502

Simplify.

(Slant height)2 = 103,041 + 22,500

(Slant height)2 = 125,541

Take square root on both sides.

(Slant height)2 = √125,541

Use calculator.

Slant height ≈ 354.32

The area of each lateral face is

= 1/2 ⋅ (base area of lateral face)(slant height)

Substitute.

≈ 1/2 ⋅ (300)(354.32)

≈ 53,148

So, the area of each lateral face is about 53,148 square feet.

3. Answer :

To find the surface area of the regular pyramid shown, start by finding the area of the base.

A diagram of the base is shown below.

The base is a regular hexagon.

Use the formula for the area of a regular polygon to find the area of the base,

= 1/2 ⋅ (apothem)(perimeter)

Substitute.

= 1/2 ⋅ (3√3)(6 ⋅ 6)

Simplify.

= 54√3 square meters

Formula for area of a regular pyramid is

S = B + 1/2 ⋅ Pl

Substitute 54√3 for the area of the base B, 36 for P and 8 for l.

S = 54√3 + 1/2 ⋅ (36)(8)

Simplify.

S = 54√3 + 144

Use calculator.

S ≈ 237.5

So, the surface area of the regular pyramid is about 237.5 square meters.

4. Answer :

Formula for surface area of a right cone is

S = πr2 + πrl

Substitute.

S = π(42) + π(4)(6)

Simplify.

S = 16π + 24π

S = 40π

Use calculator.

S ≈ 125.7

So, the surface area of the right cone is about 125.7 square inches.

5. Answer :

Formula for surface area of a right cone is

S = πr2 + πrl

Substitute.

30π = πr2 + πr(7)

Factor.

30π = π(r2 + 7r)

Divide each side by π.

30 = r2 + 7r

Subtract 30 from each side.

0 = r2 + 7r - 30

r2 + 7r - 30 = 0

Solve the above quadratic equation using factoring

(r - 3)(r + 7) = 0

r - 3 = 0 or r + 7 = 0

r = 3 or r = -7

Radius can not be negative. Then, r = 3.

So, the radius of the base of the cone is 3 inches.

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What is the surface area of the cone?

The surface area of a cone is equal to the curved surface area plus the area of the base: π r 2 + π L r , \pi r^2 + \pi L r, πr2+πLr, where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.

How to Find the slant height of a pyramid?

With the help of the Pythagorean Theorem, we can find the slant height using this formula: s² = H² + (a / 2)² , where H is the height of the square pyramid.

What is the surface area of a regular pyramid?

In order to find the total surface area, we will need to add up the areas of the base and the three other sides. SA=B+12(P×l), where B is the area of the base of the pyramid, P is the perimeter of the base, and l is the slant height of the pyramid.