Step: 1

The base area of the rectangular pyramid = length × width

Step: 2

= 13.8 × 9.2

[Substitute the values.]

Step: 3

= 126.96 cm^{2}

[Multiply 13.8 by 9.2.]

Step: 4

The volume of a rectangular pyramid = (1 3 ) × base area × height

Step: 5

= (1 3 ) × 126.96 × 11.5

[Substitute the values.]

Step: 6

= 1460.04 3

[Multiply 126.96 by 11.5.]

Step: 7

= 486.68 cm^{3}

[Divide.]

Step: 8

The base area and volume of the rectangular pyramid are 126.96 cm^{2} and 486.68 cm^{3}.

Correct Answer is : 126.96 cm^{2} and 486.68 cm^{3}

Step: 1

From the figure, the length, width and height of the rectangular pyramid are 5 cm, 4 cm and 3 cm respectively.

Step: 2

The base area of the rectangular pyramid = length × width

Step: 3

= 5 × 3

[Substitute the values.]

Step: 4

= 15 cm^{2}

[Multiply.]

Step: 5

The volume of the rectangular pyramid = (1 3 ) × base area × height

Step: 6

= (1 3 ) × 15 × 4

[Substitute the values.]

Step: 7

= 20 cm^{3}

[Simplify.]

Step: 8

The volume of the figure = 2 × volume of the rectangular pyramid

Step: 9

= 2 × 20

[Substitute volume = 212.96]

Step: 10

= 40 cm^{3}

[Multiply.]

Step: 11

∴ The volume of the figure is 40 cm^{3}.

Correct Answer is : 40 cm^{3}

Step: 1

Base of the pyramid = right triangle

Step: 2

Base area of the pyramid = area of right triangle = 1 2 × base × height = 1 2 × 6 × 6 = 18 ft^{2}.

Step: 3

Volume of the pyramid = 1 3 × base area × height

[Formula.]

Step: 4

= 1 3 × 18 × 9

[Substitute the values.]

Step: 5

= 54

[Simplify.]

Step: 6

Volume of the pyramid = 54 ft^{3}.

Correct Answer is : 54 ft^{3}

Step: 1

Height of a cube = length of each edge of a cube = 12 cm

Step: 2

Total height of the figure = height of pyramid + height of cube

15 = height of the pyramid + 12

[Substitute the values.]

Step: 3

Height of the pyramid = 3 cm

[Subtract 12 from each side.]

Step: 4

Volume of the cube = s ^{3} = 12^{3} = 1728 cm^{3}.

Step: 5

Volume of the pyramid = 1 3 × base area × height

[Formula.]

Step: 6

= 1 3 × 12^{2} × 3

[Substitute the values.]

Step: 7

= 144

[Simplify.]

Step: 8

Volume of the pyramid = 144 cm^{3}

[Simplify.]

Step: 9

Volume of the figure = volume of the cube + volume of the pyramid

= 1728 + 144 = 1872

[Substitute the values and add.]

Step: 10

Volume of the figure = 1872 cm^{3}.

Correct Answer is : 9 cm

Step: 1

Base length = 21 m

[Given.]

Step: 2

Slant height = 16 m.

Step: 3

Height of the tent = 1 6 2 - ( 2 1 2 ) 2 = 12.07 m

[Height of tent = l 2 - a 2 4 .]

Step: 4

Volume of the tent = 1 3 × 21^{2} × 12.07 = 1774.29 m^{3}

[Volume of the pyramid = 1 3 a ^{2}h .]

Step: 5

Rate of making = $60 per m^{3}

[Given.]

Step: 6

Cost of making the tent = Volume of the tent × Rate of making

[Formula.]

Step: 7

Cost of making the tent = 1774.29 × 60 = $106457.40

[Substitute in step 6 and simplify.]

Correct Answer is : $106457.40

Step: 1

Number of toys = Volume of the metallic piece Volume of one pyramid

[Formula.]

Step: 2

Volume of the metallic piece = 2 × 2 × 5 m^{3} = 20 m³

[According to the data.]

Step: 3

Height of the pyramid = 3 cm.

[Given.]

Step: 4

Length of lateral edge = 7 cm.

[Given.]

Step: 5

Lateral edge, height and half of the diagonal forms a right triangle.

[From the figure.]

Step: 6

[d 2 = Lateral side ² - h ² .]

Step: 7

d = 2 × 6.32 = 12.64

[Multiply each side by 2.]

Step: 8

Volume of one pyramid = 1 3 × 1 2 . 6 4 ² 2 × 3 = 79.88 cm^{3}

[Volume of pyramid = 1 3 × base area × height.]

Step: 9

Number of toys = 20×100×100×100 79.88 = 250376 toys (approximately)

[Substitute in step 1 and simplify.]

Correct Answer is : 250376

Step: 1

From the figure, the length, width and height of the rectangular pyramid are 7 cm, 6 cm, and 12 cm, respectively.

Step: 2

Volume of a rectangular pyramid = (1 3 ) × length × width × height

Step: 3

= (1 3 ) × 7 × 6 × 12

[Substitute the values.]

Step: 4

= 504 3 cm^{3}

Step: 5

= 168 cm^{3}

[Simplify.]

Step: 6

The volume of the rectangular pyramid is 168 cm^{3}.

Correct Answer is : 168 cm^{3}

Step: 1

[Given.]

Step: 2

3V = 3 × 1 3 × l w h .

[Multiply by 3 on each side.]

Step: 3

3V = l w h

[Simplify.]

Step: 4

[Divide each side by w h .]

Step: 5

[Simplify.]

Step: 6

Therefore, the length of the rectangular pyramid is 3 V w h .

Correct Answer is : 3 V w h

Step: 1

[Given.]

Step: 2

3V = 3 × 1 3 × l w h

[Multiply by 3 on each side.]

Step: 3

3V = l w h

[Simplify.]

Step: 4

[Divide each side by l h .]

Step: 5

[Simplify.]

Step: 6

Therefore, the width of the rectangular pyramid is 3 V l h .

Correct Answer is : 3 V l h

Step: 1

The volume of the rectangular pyramid = 1 3 × base area × height

[Volume formula.]

Step: 2

The height of the rectangular pyramid = 3 × v o l u m e b a s e a r e a .

Step: 3

= 3 × 396 108

[Substitute.]

Step: 4

= 3 × 11 3 = 11

[Simplify.]

Step: 5

Therefore, the height of the rectangular pyramid is 11 cm.

Correct Answer is : 11 cm

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