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3 years ago

6

A sculpture at a park is in the shape of a rectangular pyramid. What is the volume of the sculpture if the length and width of t

he base of the pyramid are 11 feet and 5 feet respectively, while the height of the pyramid is 6 feet?

1 answer:

sweet [91]3 years ago

4 0

Answer:

40

Step-by-step explanation:

11x6=60

60-5x4= 20

=40

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Field book of an land is given in the figure. It is divided into 4 plots . Plot I is a right triangle , plot II is an equilatera

Kazeer [188]

Answer:

Total area = 237.09 cm²

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Field book of an agricultural land is given in the figure. It is divided into 4 plots. Plot I is a right triangle, plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium, Find the area of each plot and the total area of the field. ( use √3 =1.73)

From the figure attached,

Area of the right triangle I = $\frac{1}{2}(\text{Base})\times (\text{Height})$

Area of ΔADC = $\frac{1}{2}(\text{CD})(\text{AD})$

= $\frac{1}{2}(\sqrt{(AC)^2-(AD)^2})(\text{AD})$

= $\frac{1}{2}(\sqrt{(13)^2-(19-7)^2} )(19-7)$

= $\frac{1}{2}(\sqrt{169-144})(12)$

= $\frac{1}{2}(5)(12)$

= 30 cm²

Area of equilateral triangle II = $\frac{\sqrt{3} }{4}(\text{Side})^2$

Area of equilateral triangle II = $\frac{\sqrt{3}}{4}(13)^2$

= $\frac{(1.73)(169)}{4}$

= 73.0925

≈ 73.09 cm²

Area of rectangle III = Length × width

= CF × CD

= 7 × 5

= 35 cm²

Area of trapezium EFGH = $\frac{1}{2}(\text{EF}+\text{GH})(\text{FJ})$

Since, GH = GJ + JK + KH

17 = $\sqrt{9^{2}-x^{2}}+5+\sqrt{(15)^2-x^{2}}$

12 = $\sqrt{81-x^2}+\sqrt{225-x^2}$

144 = (81 - x²) + (225 - x²) + 2 $\sqrt{(81-x^2)(225-x^2)}$

144 - 306 = -2x² + $2\sqrt{(81-x^2)(225-x^2)}$

-81 = -x² + $\sqrt{(81-x^2)(225-x^2)}$

(x² - 81)² = (81 - x²)(225 - x²)

x⁴ + 6561 - 162x² = 18225 - 306x² + x⁴

144x² - 11664 = 0

x² = 81

x = 9 cm

Now area of plot IV = $\frac{1}{2}(5+17)(9)$

= 99 cm²

Total Area of the land = 30 + 73.09 + 35 + 99

= 237.09 cm²

7 0

3 years ago

2/x multiplied by what equals 1

Varvara68 [4.7K]

Answer:

Multiplied by2x

2/x ×2x =1

5 0

3 years ago

Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 9 inches, and t

MatroZZZ [7]

To solve this problem, you must follow the proccedure below:

1. T<span>he block was cube-shaped with side lengths of 9 inches and to calculate its volume (V1), you must apply the following formula:

V1=s</span>³
<span>
s is the side of the cube (s=9)

2. Therefore, you have:

V1=s</span>³
V1=(9 inches)³
V1=729 inches³
<span>
3. The lengths of the sides of the hole is 3 inches. Therefore, you must calculate its volume (V2) by applying the formula for calculate the volume of a rectangular prism:

V2=LxWxH

L is the length (L=3 inches).
W is the width (W=3 inches).
H is the heigth (H=9 inches).

4. Therefore, you have:

V2=(3 inches)(3 inches)(9 inches)
V2=81 inches
</span><span>
5. The amount of wood that was left after the hole was cut out, is:
</span>
Vt=V1-V2
Vt=648 inches³

7 0

3 years ago

a how much will he have in 4. At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi

Natalka [10]

Answer:

6795.70

Step-by-step explanation:

smart people

6 0

2 years ago

Mr. Douglas drove 2,482 miles. He spent 42.5 hours in the car driving. What was his avrage speed for the trip?

Readme [11.4K]

Use the formula speed=distance/time, or s=d/t.

Substitute 2,482 for d and 42.5 for t.

s=2,482/42.5

Simply divide for the answer:

Mr. Douglas' average speed for the trip was 58.4 miles per hour.

I hope this helps! ^_^

4 0

3 years ago