Please help!!...............................

Mathematics

1 answer:

Airida [17]3 years ago

3 0

B. you have to be ready to multiply all the numbers to get your answer.

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3 years ago

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2 years ago

Help 80 points A concrete planter is formed from a square-based pyramid that was inverted and placed

Rufina [12.5K]

Answer:

The slant height of the pyramid refers to the height of a face of the pyramid.

Notice that each slant height forms a right triangle like the image attached shows, where the hypothenuse is the slant height. Additionally, the bottom leg is 1 yard, because is half of the base side, and the other leg is 2 yard. Using Pythagorean's Theorem, we have

$h^{2} =1^{2} +2^{2} \\h=\sqrt{1+4}=\sqrt{5}$

Therefore, the slant height is the square root of 5 yard.

The surface area of the composite figure is the sum of the surface area of both volumes.

<h3>Surface area of the cube.</h3>

$S_{cube}=5(2yd)^{2} =20 yd^{2}$

Notice that we only included 5 faces of the cube, that is because the sixth is the base of the pyramid, so if we include it here, we would have the wrong total surface area.

<h3>Surface area of the pyramid.</h3>

$S_{pyramid}=\frac{1}{2}pl$

Where $p$ is the perimeter of the base and $l$ is the slant height.

$S_{pyramid}=\frac{1}{2}(8yd)(\sqrt{5}yd )=4\sqrt{5}yd ^{2}$

Therefore, the surface od the composite figure is

$S_{total}=20yd^{2} +4\sqrt{5} yd^{2} \approx 29.94 yd^{2}$

To find the cubic yards of concrete, we need to subtract the volume of the figures, because the concrete would be inside the space between the cube and the pyramid.

$V_{concrete}=V_{cube} -V_{pyramid}=l^{3}- \frac{1}{3}l^{2}h$