A circular tent is in the form of a cone over a cylinder. The diameter of the base is 9m, the height of the cylindrical part is 4.8m and the total height of the tent is 10.8m. The canvas required for the tent is______

Chapter/Topic: Surface Areas and Volumes

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

24.184 m2

2418.4 m2

241.84 m2

None of these

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Curved surface area of the cylinder is 2πrh
Height of a cylinder is h=4.8m
Diameter of a cylinder is d=9m
Then, radius r=

\frac{9}{2}

=4.5m
Curved surface area of cylinder =2πrh
=2×π×4.5×4.8

=2×

\frac{9}{2}

×21.6

=135.77m2
seo

Curved surface area of cone is =πrl
As we can see in the figure the radius is the same for cylinder and cone. Slant height is given by l=

\sqrt{h^{2} + r^{2}}

is the height of the cone. Height of cone=total height of tent- height of cylinder.
That is h=10.8−4.8=6
l=

\sqrt{6^{2} + {4.5}^{2}}

.
⇒l=7.5m
Curved surface area of cone is = πrl
=

\frac{22}{7}

×4.5×7.5
                                                       = 106.07m2
Area of canvas= curved surface area of cylinder +curved surface area of cone                                135.77+106.07
                                                   = 241.84 m2
Hence, Area of canvas = 241.84 m2                         Hence, Option (3) is the correct answer.

Watch 3-min video & get full concept clarity