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djverab [1.8K]
3 years ago
11

Dana is given the total surface area of a rectangular pyramid. She is asked for the lateral surface area. Describe how Dana can

use the given information to determine the lateral surface area.
Mathematics
1 answer:
irina [24]3 years ago
8 0

To get the lateral surface area, dana will subtract the two base area from the total surface area.

<h3>Total surface area of rectangular prism</h3>

The total surface area of a rectangular prism is the sum of the areas of all of the faces or surfaces that enclose the solid. Therefore,

  • 2lw + 2wh + 2lh

where

l = length

w = width

h = height

<h3>Lateral surface area of a rectangular prism</h3>

The lateral surface area of a rectangular prism is the surface area of the solid without the bases.

Therefore,

  • LA =  2 ( l + w ) h

Total surface area = Lateral surface area + 2 (Base Area)

Total surface area =  2 (l + w) h + 2 (l x w) = 2lh + 2wh + 2lw

Therefore,

Lateral surface area = Total surface area - 2 (Base Area)

To get the lateral surface area, dana will subtract the two base area from the total surface area.

learn more on rectangular pyramid here: brainly.com/question/3096481

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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round
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The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying  \frac{1}{3} with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone :  V=\pi r^{2} \frac{h}{3} = 3.14 \times 9^{2} \times \frac{14}{3} = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying  \frac{4}{3} with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere =  V=\frac{4}{3} \pi r^{3} =  \frac{4}{3} \times 3.14 \times 9^{3} = 3,052.08 cubic inches.

The volume of the half-sphere =  \frac{3,052.08}{2} = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

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