A decorative block which is made of two solids , a cube and a hemisphere. The base of the block is a cube with edge 5 cm , and the hemisphere fixed on the top has a diameter 4.2 cm.Find the total surface area of the block .
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)
Answers
Answered by
165
SOLUTION:
The decorative block is a combination of a cube and the hemisphere.
For cubical portion:
Each edge= 5 cm
For hemispherical portion:
Diameter= 4.2 cm
Radius(r)= 4.2/2= 2.1 cm
Total surface area of the cube= 6 × (edge)²
= 6 (5)²= 6 × 25= 150 cm²
Here the part of the cube where the hemisphere is attached is not included in the surface area.
So the total surface area of the decorative block= total surface area of the cube+ area of base of hemisphere + curved surface area of hemisphere
total surface area of the decorative block= 150 - πr² + 2πr²
= 150 +πr²
= 150 + (22/7) × 2.1× 2.1
= 150 + 13.86 = 163.86cm²
Hence,total surface area of the decorative block=163.86 cm²
HOPE THIS WILL HELP YOU....
The decorative block is a combination of a cube and the hemisphere.
For cubical portion:
Each edge= 5 cm
For hemispherical portion:
Diameter= 4.2 cm
Radius(r)= 4.2/2= 2.1 cm
Total surface area of the cube= 6 × (edge)²
= 6 (5)²= 6 × 25= 150 cm²
Here the part of the cube where the hemisphere is attached is not included in the surface area.
So the total surface area of the decorative block= total surface area of the cube+ area of base of hemisphere + curved surface area of hemisphere
total surface area of the decorative block= 150 - πr² + 2πr²
= 150 +πr²
= 150 + (22/7) × 2.1× 2.1
= 150 + 13.86 = 163.86cm²
Hence,total surface area of the decorative block=163.86 cm²
HOPE THIS WILL HELP YOU....
Answered by
93
Hi!
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Total Surface area of the Cube
6 * (edge)^2
6 * (5)^2
6 * 5 * 5 cm^2
150 cm^2
The Surface area of the block
TSA of Cube - base area of hemisphere + CSA of hemisphere
= 163.86 cm^2
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Thanks !!
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