Prism Solve for h

Prism is one of the three dimensional shape. Normally the prisms faces are flat surface. Here we have two bases, one is at the top and another is at the bottom. In prisms we have two kinds of prisms; they are rectangular prism and triangular prism. When a prism bottom is rectangular shape then it’s denoted as rectangular prism. Cube and cuboids are some examples are rectangular prism. When a prism bottom is triangular shape then its said to be triangular prism. 

The diagram given below the structure of prism:

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Description to prism solve for h:

The following types are used in the prism shape they are

Volume of the regular prism is = BH cubic units,

Where B represents the base area of shape, and H represents height.

The Lateral surface area of the regular prism is given by,

              L.S.A = PH square units.

Where P represents the perimeter of shape and H represents the height of prism

Prism based on rectangular:

The area of the base is calculated by l*w

The perimeter of the base can be calculated by 2(l+w)

Therefore the total surface area is calculated by 2lw+2(l+w)H

Volume of the rectangular prism is V= L * W * H

Triangular based prism:

The area is measured as 1/2 bh

The perimeter of the base is measured by a+b+c.

So the surface are is measured by  bh+ (a+b+c) H

Circular based prism:

The area of the base is calculated as `pi` r²

The perimeter of the base is calculated by 2`pi` r

Therefore the surface area of the prism is 2`pi` r²+2`pi` rH

Let we see some basic problems regarding prisms.

Example 1:

 The dimensions of the rectangular prism is given below ,they are length is 10cm, height is 4 cm, and width is 14 cm.

Solution:

Given dimensions length = 10 cm, height = 4 cm, width = 14 cm.

Formula:

  Surface area = 2lw+2(l+w)H

apply  the values in the above formula, we get

                       = 2 *10*14+2(10+14)4

                       = 240 + 2(24)4

                      = 240 + 48*4

                     = 240 +192

                     = 432 cm²

      Volume = l * w * h  

                      = 10 * 4 * 14 cm³

                      = 560 cm³

Answer:

Surface area = 432 cm²

Volume = 560 cm³

Examples problems to solve h in prism

Example 1:

solve the h value whose prism volume is 1210 cubic units and base is 21 cm.

Solution:

The volume of the prism is V = 1210cubic units.

Base of the prism is = 21cm

                                   V= BH

apply the values in the formula we get

                              1210 = 121*H

                                     h = 1210 /121

                                     h = 10cm.

Example2:

The volume of the  rectangular prism is 360 cm³ and its length and widths are 10 ,4 cm , solve the h value

Solution:

The volume of the rectangular prism is V = 360cm³

Length of the rectangular prism is l = 10cm

Width of the rectangular prism is W = 4 cm

Apply these values in formula we get

                                     360 = 10*4*h

                                      360 = 40 *h

                                     h = 360 / 40

                                    h = 9 cm

Sample problems:

1) The volume of a regular prism is  120cm³.The base of the regular prism is 10 cm , solve its height h?

solution : height h = 12 cm.

2) The volume of the rectangular prism is 420cm3 and its length = 7 cm and width =6 cm and solve its height h?

solution: height h = 10 cm.