A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid after the cone is carved out.
Answers
Answer :
1022 + 154√5
Step-by-step explanation :
Edge of Cube = 14 cm
Cone of maximum size is carved.
So, Diameter of cone = Edge of Cube = 14 cm
Height of cone = Edge of Cube = 14 cm.
Radius of cone = 14 / 2 = 7 cm.
Surface area of solid = Area of Cube + CSA of cone - Base area of cone .
Find Area of Cube ;
Here, side = 14 cm
Area of Cube = 6 ( side )²
= 6 × 14²
= 6 × 196
= 1176 cm²
Find Slant Height of cone ;
Radius of cone = 7 cm
Height of cone = 14 cm
We need to find slant height ( l )
l = √ r² + h²
l = √ 7² + 14²
l = √ 7² + ( 7 × 2 )²
l = √ 7² ( 1 + 2² )
l = 7 √ ( 1 + 2 )²
l = 7 √ ( 1 + 4 )
l = 7 √ 5 cm
Find CSA of cone ;
CSA of cone = π r l
= π × 7 × 7√5
= 22 × 7 × √5
= 154√5 cm²
Find base area of cone ;
Base of cone is a circle with Radius = Radius of cone = r = 7
Base area of cone = π r²
= 22 / 7 × 7²
= 22 × 7
= 154 cm²
Now,
Surface area of solid = Area of Cube + Curved surface area of cone - Base area of cone
= 1176 + 154√5 - 154
= 1022 + 154√5
Hence, the answer is 1022 + 154√5 .
