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Chapter 12: Q30. (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(72xy+64x2) cube unit and the surface area is 96x2ysquare unit.

Step by step solution

01

Step 1. Given information.

A figure provided in the question,

02

Step 2. Determine the Surface Area.

To find the surface area, first find the lateral area sand base area,

L.A.=ph=(8x+16x)3y[substitute]=72xy[simplify]

And

B=(6x)2−4x2=36x2−4x2[multiply]=32x2[subtract]

Thus, the total surface area is.

T.A.=L.A.+2B=72xy+64x2[simplify]

So, the surface area is72xy+64x2 .

03

Step 3. Determine the Volume.

Now find the volume, multiply the base area by height.

v=32x2(3y)=96x2y[multiply]

Thus, the volume is96x2y .

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Most popular questions from this chapter

Accurately draw or construct a large equilateral triangle. Choose any point inside the triangle and carefully measure the distance x, y, z and h. Then findx+y+z.

Find the following for the regular triangular pyramid.

  1. If BC = 6, find AM and AO.
  2. If BC = 6 and VA = 4, find h and l.

Find the following for the regular triangular pyramid.

a.If h = 4 and l = 5, find OM, OA and BC.

b.Find the lateral area and the volume.

What kind of figure in each lateral face in the following prism?

Sketch the following pyramid. Then find its lateral area.

A regular triangular pyramid with base edge 4 and slant height 6.
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