about its longest side as axis

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Nov 28, 2013 11:30 pm

A triangle of dimensions 6, 8, and 10 is rotated about its longest side as axis. Which of the following is nearest to the curved surface area of the solid so generated?
A. 120
B. 150
C. 180
D. 210
E. 240

Made Up

An example situation to the question is this figure.

Courtesy https://gknowledgecbse10.blogspot.in

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Sanjeev K Saxena
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Source: Beat The GMAT — Problem Solving | Thu Nov 28, 2013 11:30 pm

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Fri Nov 29, 2013 5:16 am

Hi Sanju09,
Is Answer D ?

Regards,
Uva

Known is a drop Unknown is an Ocean

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Fri Nov 29, 2013 8:56 am

The maximum radius is R = 4.8 (see diagram).

The curved surface area of a cone is pi * R * L where L = slant height.

We have 2 cones:

So total surface area = pi * R * (L1 + L2)
= 3.14 * 4.8 * (6 + 8) = 211 (approx.)

Answer = (D)

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Nov 29, 2013 11:36 pm

Please draw on your own according to the following explanation:

âˆ†ABC has AB = 6, BC = 10, and CA = 8, and consequently it is right angled at A. Mathsbuddy did justice to the situation that I described in the question. Now drop perpendicular from A on BC to meet BC in D. This AD would serve as the common radius in the resulting solid so generated. Area of âˆ†ABC is Â½ AB.AC = Â½ BC.AD = 24, hence AD = 4.8; for approximation purposes we'll later on take AD = 5.

The curved surface area of a cone = Ï€ (Base Radius) (Slant Height)

[Let's take Ï€ = 3 only]

The collective curved surface area of the solid so generated would equal

Ï€(5)(6) + Ï€(5)(8) = [spoiler]90 + 120 = 210. It's D.[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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