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Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Volume of Pyramid

Grade: 4-a Lesson: S3-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Given a square pyramid with a lateral surface area of 288 meters², slant height of 12 meters, and height of 8 meters, find its volume.
2	Step	The given values of the square pyramid is	LA = 288 \$meter^2\$ l = 12 meters h = 8 meters
3	Formula	The lateral surface area of square pyramid is	LA = \$1/2 times 4s times l\$
4	Step	Substitute the values in the formula we get the base length"s"	288 = \$1/2 times 4s times 12\$ 288 = \$6 times 4s\$ 288 = 24s
5	Step	After simplification by moving the "s" coefficient into right hand side	\$288/24\$ = s 12 = s
6	Formula	The volume of the square pyramid is	V = \$1/3 times a times h\$
7	Step	The base area of the pyramid is the product of sides	a = \$s times s\$ a = \$s^2\$
8	Step	Substitute the values in the above formula ,we get base area	a = \$12 times 12\$ a = 144
9	Step	The Base area of the square pyramid is	144 \$meters^2\$
10	Step	Substitute the all values in the volume formula	V = \$1/3 times 144 times 8\$ V = \$1/3 times 1152\$ V = \$1152/3\$ V = 384
11	Step	The volume of the square pyramid is 384 \$meter^3\$.
12	SumUp	Can you summarize what you’ve understood in the above steps?
13	Choice.A	This is not correct because it provides an incorrect value for the volume	356 \$meters^3\$
14	Choice.B	This is not correct because it provides an incorrect value for the volume	405 \$meters^3\$
15	Choice.C	This is correct because it correctly calculates the volume of the square pyramid	384 \$meter^3\$
16	Choice.D	This is not correct because it provides an incorrect value for the volume	398 \$meters^3\$
17	Answer	Option	C
18	SumUp	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Given a square pyramid with a lateral surface area of 288 meters², slant height of 12 meters, and height of 8 meters, find its volume.

Step

The given values of the square pyramid is

LA = 288 \$meter^2\$
l = 12 meters
h = 8 meters

Formula

The lateral surface area of square pyramid is

LA = \$1/2 times 4s times l\$

Step

Substitute the values in the formula we get the base length"s"

288 = \$1/2 times 4s times 12\$

288 = \$6 times 4s\$

288 = 24s

Step

After simplification by moving the "s" coefficient into right hand side

\$288/24\$ = s

12 = s

Formula

The volume of the square pyramid is

V = \$1/3 times a times h\$

Step

The base area of the pyramid is the product of sides

a = \$s times s\$

a = \$s^2\$

Step

Substitute the values in the above formula ,we get base area

a = \$12 times 12\$

a = 144

Step

The Base area of the square pyramid is

144 \$meters^2\$

Step

Substitute the all values in the volume formula

V = \$1/3 times 144 times 8\$

V = \$1/3 times 1152\$

V = \$1152/3\$

V = 384

Step

The volume of the square pyramid is 384 \$meter^3\$.

SumUp

Can you summarize what you’ve understood in the above steps?

Choice.A

This is not correct because it provides an incorrect value for the volume

356 \$meters^3\$

Choice.B

This is not correct because it provides an incorrect value for the volume

405 \$meters^3\$

Choice.C

This is correct because it correctly calculates the volume of the square pyramid

384 \$meter^3\$

Choice.D

This is not correct because it provides an incorrect value for the volume

398 \$meters^3\$

Answer

Option

SumUp

Can you summarize what you’ve understood in the above steps?