Question

the top of the solid cone of height 12cm and base radius 6 CM ,a cone of height 4 cm is removed by a plane parallel to the base find the total surface area of the remaining solid used by 22 /7 and root √5= 2.236​

Answer 1

Answer:

Step-by-step explanation:

Brainly.in

What is your question?

anushya155

Secondary School Math 5+3 pts

A solid cone of height 12 cm and base radius 6 cm has the top 4 cm removed. Find the whole surface area of remaining figure.

Report by Dishu619 13.02.2018

Answers

abhi178

Abhi178★ Brainly Teacher ★

A cone of radius CD and height AD as shown in figure is cut from the top of 4cm at point E.

now, AD = 12cm , CD = 6cm , AE = 4cm

here it is clear that ∆ABE ~ ∆ACD

so, AE/AD = BE/CD

4cm/12cm = BE/6cm

BE = 2 cm { it is the radius of small circular part , Let r }

now, whole surface area of remaining part of cone = lateral 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) × 22/7 cm²

= 350.59 cm²

Click to let others know, how helpful is it

4.0

143 votes

THANKS 220

nikitasingh79

Nikitasingh79★ Brainly Teacher ★

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

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 = 350.59 cm²

Hence, the Total surface area of the remaining cone = 350.59 cm²

Hope it's useful for you

Answer 2

Step-by-step explanation:

hope it helps you follow me.....