Question

learning activity sheetlearning area: mathematicsquarter: 2lesson no.: 3date:lesson title/ topic: volume of a square pyramid and rectangular pyramidname:grade & section:i. activity no. 3: (15 minutes)ii. objective(s): at the end of the lesson, the students are able to:a. find the volume of a square pyramid and a rectangular pyramid; andb. solve problems involving volume of a square pyramid and a rectangular pyramid.iii. materials needed: activity sheet, peniv. instructions:a. solve for the following problem:1. find the volume of a pyramid with a rectangular base measuring 6 cm by 9 cm and height 19 cm.2. a square pyramid has a height of 17 m and a base that measures 12 m on each side. find the volume of the pyramid.3. a rectangular pyramid has a base with dimensions of 9 meters and 13 meters respectively and its height measures 15 meters. find the volume of the pyramid.4. what is the volume of a pyramid whose square base has a length of 15 inches and a height of 21 inches?5. find the volume of a pyramid whose base dimensions are 11 and 15 inches and whose height is 21 inches.mathematics 8 quarter 24pilot implementation of the matatag k to 10 curriculumb. find the volume of the following figures.1.2.3.

Explanation:

The formula for the volume of a pyramid is $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height of the pyramid.

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Part A: Solve the word problems

Problem 1:

Step1: Calculate base area

$B = 6\ \text{cm} \times 9\ \text{cm} = 54\ \text{cm}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 54\ \text{cm}^2 \times 19\ \text{cm}$
$V = 18 \times 19 = 342\ \text{cm}^3$

Problem 2:

Step1: Calculate base area

$B = 12\ \text{m} \times 12\ \text{m} = 144\ \text{m}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 144\ \text{m}^2 \times 17\ \text{m}$
$V = 48 \times 17 = 816\ \text{m}^3$

Problem 3:

Step1: Calculate base area

$B = 9\ \text{m} \times 13\ \text{m} = 117\ \text{m}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 117\ \text{m}^2 \times 15\ \text{m}$
$V = 39 \times 15 = 585\ \text{m}^3$

Problem 4:

Step1: Calculate base area

$B = 15\ \text{in} \times 15\ \text{in} = 225\ \text{in}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 225\ \text{in}^2 \times 21\ \text{in}$
$V = 75 \times 21 = 1575\ \text{in}^3$

Problem 5:

Step1: Calculate base area

$B = 11\ \text{in} \times 15\ \text{in} = 165\ \text{in}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 165\ \text{in}^2 \times 21\ \text{in}$
$V = 55 \times 21 = 1155\ \text{in}^3$

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Part B: Find volume of figures

Figure 1:

Step1: Calculate base area

$B = 9\ \text{cm} \times 9\ \text{cm} = 81\ \text{cm}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 81\ \text{cm}^2 \times 15\ \text{cm}$
$V = 27 \times 15 = 405\ \text{cm}^3$

Figure 2:

Step1: Calculate base area

$B = 7\ \text{m} \times 15\ \text{m} = 105\ \text{m}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 105\ \text{m}^2 \times 12\ \text{m}$
$V = 35 \times 12 = 420\ \text{m}^3$

Figure 3:

Step1: Calculate base area

$B = 13\ \text{ft} \times 7\ \text{ft} = 91\ \text{ft}^2$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 91\ \text{ft}^2 \times 18\ \text{ft}$
$V = 91 \times 6 = 546\ \text{ft}^3$

Answer:

Part A

1. $342\ \text{cm}^3$
2. $816\ \text{m}^3$
3. $585\ \text{m}^3$
4. $1575\ \text{in}^3$
5. $1155\ \text{in}^3$

Part B

1. $405\ \text{cm}^3$
2. $420\ \text{m}^3$
3. $546\ \text{ft}^3$