In the given fig from the top of a solid cone of height 12cm and base radius 6cm, a cone of height 4cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid(Use 
√5=2.236)
Answers
Answer:
Step-by-step explanation:
SOLUTION :
Given:
AB= 4 cm, AC= 12 cm, CD = 6 cm
In Δ ABE and Δ ACD,
BE || CD
∠AEB= ∠ADC [each 90°]
∠ABE= ∠ACD [ corresponding angles]
Δ ABE ∼ Δ ACD [By AA Similarity]
AB/AC = BE/CD
[Corresponding sides of a similar triangles are proportional]
4/12 = BE /6
1/3 = BE/6
1 = BE/2
BE = 2
In ∆ACD
AD² = AC² + CD²
AD² = 12² + 6²
AD² = 144 + 36
AD² = 180
AD = √180 = √36 ×5 = 6√5 = 6×2.236
Slant height of bigger cone AD = 13.416 cm
Total surface area of bigger cone with radius 6 cm = πr(l + r)
= π×6(6 + 13.416)
= π×6×19.416 = π(116.496) cm²
Total surface area of bigger cone with radius 6 cm = π(116.496) cm²
Slant height of smaller cone (l) =√h²+r² √(AB²+BE² )
l = √(4²+ 2²)
l = √(16 + 4)
l = √20 =√4×5=2×2.236
l = 4.472 cm
Curved surface area of smaller cone of height 4 cm and radius 2 cm = πrl
= π×2×4.472 = π(8.944) cm
Total surface area of the remaining cone = Total surface area of bigger cone - curved surface area of smaller cone + area of base of smaller cone
= π(116.496) - π(8.944) + πr²
= π(116.496) - π(8.944) + π(2)²
= π(116.496 - 8.944 +4)
= π(107.552 +4) = π (111.552) cm
= 22/7(111.552)
= 2,454.144 /7
Total surface area of the remaining cone = 350.59 cm²
Hence, the Total surface area of the remaining cone = 350.59 cm²
HOPE THIS ANSWER WILL HELP YOU…..
ANSWER:------
{surface area of frustum + area of above circular part + area of below circular part }
{= πl(R + r) + πr² + π R² }
{where, l = √{h² + (R - r)²}
{here, h = 12cm - 4cm = 8 cm }
{so, l = √{8² + (6-2)²} = √{64 + 16} = 4√5cm}
{now, whole surface area = π × 4√5 × (6 +2) + π × (6)² + π × (2)² }
©©©= 32√5π + 36π + 4π cm²
©©©= (32√5 + 40)π cm²
©©©= (32 × 2.236 + 40) × 22/7cm²
©©©= answer below /
--------350.59 cm²
hence proved:-----
hope it helps:------
T!—!ANKS!!!