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Chapter 12: Q29. (page 479)

Find the volume and the total surface area of each solid in terms of the given variables.

Short Answer

Expert verified

The volume is 50x3and the surface area is 120x2.

Step by step solution

01

Step 1. Given information.

A figure provided in the question,

02

Step 2. Determine values.

Firstly, for finding the volume of the solid, subtract the volume from the total volume.

v=(4x×3x)(5x)−(x×2x)(5x)=60x3−10x3[multiply]=50x3[subtract]

Thus, the volume of the solid is .

Now find the surface area, add the all area.

40x2+30x2+20x2+10x2+20x2=120x2

Thus, the surface area is120x2 .

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Most popular questions from this chapter

If the length and width of a rectangular solid are each decreased by 20%, by what percent must the height be increased for the volume to remain unchanged? Give your answer to the nearest whole percent.

The diagonals of a cube intersect to divide the cube into six congruent pyramids. Thatbase of each pyramid is a face of the cube, and height of each pyramid is 12e.

  1. Use the formula for the volume of a cube to explain why the volume of each pyramid is V=16e3.
  2. Use the formula in part (a) to show that V=13Bh.

Now choose another point on or inside the triangle and findx+y+z. What do you notice? Why does this happen?

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

l6w4h2L.A.T.A.V

Sketch the following square pyramid described. Then find its lateral area, total area, and volume.

Base  edge=16,  Slant  Height=10
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