Question

The total surface area of the combined figure i.e. hemispherical dome with

radius 14m and cuboidal shaped top with dimensions 8m 6m 4m is​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

A hemispherical dome with a radius of 14m and cuboidal shaped top with dimensions of 8m 6m 4m.

To Find:

The total surface area of the combined figure is hemispherical done and cuboidal top.

Solution:

To find the total surface area of the combined figure we will follow the following steps:

As we know,

The formula for the total Surface area of the hemisphere = 2π r².

The formula of cuboidal shaped top = 2 (length× breadth + breadth× height + height× length).

The total area of the figure = Area of hemisphere + area of cuboidal top = 2πr² + 2 (length× breadth + breadth× height + height× length) - length× breadth.

One face of the cuboidal top is subtracted because it is joined with the hemisphere and is repeated if not subtracted.

The length, breadth and height of the cuboidal top are 8m, 6m and 4m respectively.

Now, putting values in the above formula we get,

Value of π = 22/7.

Total area =2π(14)² + 2(8×6 + 6×4+ 4×8)-8×6 = 1232 + 2(48+24+32) - 8×6 = 1232 + 2(104) - 48 = 1232 + 208 -48 = 1392.0 metres square.

Henceforth, the total surface area of the combined figure hemispherical dome and the cuboidal top is 1392.0 metres square.