A small hemisphere of radius 4 cm is mounted on a larger hemisphere of radius7 cm with common base. Find the surface area and volume of the combinedfigure. (Take n = 3.14)​

Answers 2

Answer:

combined surface area =  511.82 cm²

combined volume = 851.97 cm³

Step-by-step explanation:

given, radius of small hemisphere = 4 cm

radius of large hemisphere = 7 cm

total surface area of hemisphere = 3πr²

TSA of large hemisphere = 3 × 3.14 × 7² = 461.58 cm²

Curved surface area of hemisphere = 2πr²

CSA of small hemisphere = 2 × 3.14 ×  4² = 100.48 cm²

base area of small hemisphere = πr² = 3.14 × 4² = 50.24 cm²

surface area of the combined figure = TSA of large hemisphere +CSA of small hemisphere - base area of small hemisphere

combined surface area = 461.58 + 100.48 - 50.24 = 511.82 cm²

combined surface area = 511.82 cm²

volume of hemisphere = πr³

volume of small hemisphere =  × 3.14 × 4³ =  133.97 cm³

volume of large hemisphere =  × 3.14 × 7³ = 718 cm³

combined volume = volume of small hemisphere +volume of large hemisphere = 133.97 + 718 = 851.97 cm³

combined volume = 851.97 cm³

i hope that this will help u!!!

Concept

Total surface area of the hemisphere = 3πr2 square units

Where π is a constant whose value is equal to approximately 3.14. "r" is the radius of the hemisphere.

The volume of a hemisphere is derived from Archimedes. Volume of hemisphere = (2/3)πr^3 cubic units.

Given

It is given that a small hemisphere of radius 4 cm is mounted on a larger hemisphere of radius 7 cm with common base.

Find

We need to find the surface area and volume of the combined figure

Solution

Let us assume the radius of smaller hemisphere as r1 and the radius of larger hemisphere as r2

r1=4 cm and r2=7 cm

The surface area of combined figure is= Total surface area of smaller hemisphere+ Total surface area of larger hemisphere -area of base of smaller hemisphere

=3π r1^2 + 3π r2^2 - π r1^2

=3* 3.14* 4^2 + 3* 3.14* 7^2 - 3.14 * 4^2

=562.06 cm^2

The volume of the combined figure = (2/3) *π* r1^3 + (2/3) *π* r2^3

=((2/3) *3.14* 4^3 + (2/3) *3.14* 7^3

=851.9867 cm^3

Hene the surface area of combined figure is 562.06 cm^2 and the volume of the combined figure is 851.9867 cm^3

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