JIPMAT 2021 (QA) - The length of canvas 1.1 m wide required to build a conical tent of height 14m and the floor area 346.5 m^2 is | PYQs + Solutions

JIPMAT 2021

Geometry

Solids

Conceptual

The length of canvas 1.1 m wide required to build a conical tent of height 14m and the floor area 346.5 $m^{2}$ is

490 m

525 m

665 m

860 m

Correct Option: 2

Let's solve this step by step:

Area of floor =

346.5

m^2

Floor is circular, so using area formula:

\newline

346.5 = \pi r^2

Radius of floor =

r = \sqrt{\frac{346.5}{\pi}} = 10.5

Height of tent =

h = 14

Slant height using Pythagoras theorem:

\newline

l = \sqrt{h^2 + r^2} = \sqrt{14^2 + 10.5^2} = \sqrt{196 + 110.25} = \sqrt{306.25} = 17.5

Area of curved surface =

\pi r l

= \pi × 10.5 × 17.5 = 577.5

^2

Width of canvas =

1.1

Length of canvas required =

\frac{577.5}{1.1} = 525

The answer is

525