Curved surface area of a cone with base radius $40$ cm is $1640 π$ sq. cm. Find the height of the cone in cm.

Question

Curved surface area of a cone with base radius $40$ cm is $1640 π$ sq. cm. Find the height of the cone in cm.

Answer 1

Curved surface area of a cone $= π r l$
Hence, curved surface area of this cone $= π \times 40 \times l = 1640 π$
$\Rightarrow l = 41 c m$
For a cone, $l = h^{2} + r^{2}$
Hence, $41 = h^{2} + 4 0^{2}$
$\Rightarrow 1681 = h^{2} + 1600$

$\Rightarrow h^{2} = 81$
$\Rightarrow h = 9 c m$

Answer 2

Curved surface area of a cone $= π r l$
Hence, curved surface area of this cone $= π \times 40 \times l = 1640 π$
$\Rightarrow l = 41 c m$

For a cone, $l = h^{2} + r^{2}$

Hence, $41 = h^{2} + 4 0^{2}$

$\Rightarrow 1681 = h^{2} + 1600$

$\Rightarrow h^{2} = 81$

$\Rightarrow h = 9 c m$

Curved surface area of a cone with base radius $40$ cm is $1640 π$ sq. cm. Find the height of the cone in cm.

Answer

Curved surface area of a cone $= π r l$
Hence, curved surface area of this cone $= π \times 40 \times l = 1640 π$
$\Rightarrow l = 41 c m$
For a cone, $l = h^{2} + r^{2}$
Hence, $41 = h^{2} + 4 0^{2}$
$\Rightarrow 1681 = h^{2} + 1600$

$\Rightarrow h^{2} = 81$
$\Rightarrow h = 9 c m$

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Class 10 Geometry Chapter 5 to 6

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Curved surface area of a cone with base radius 40 cm is 1640π sq. cm. Find the height of the cone in cm.

Answer

Curved surface area of a cone =πrl Hence, curved surface area of this cone =π×40×l=1640π ⇒l=41cmFor a cone, l=h2+r2​Hence, 41=h2+402​⇒1681=h2+1600 ⇒h2=81⇒h=9cm

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Take Toppr Scholastic Test for Aptitude and Reasoning

Win exciting scholarships and plan a great education plan

Curved surface area of a cone with base radius $40$ cm is $1640 π$ sq. cm. Find the height of the cone in cm.

Curved surface area of a cone $= π r l$
Hence, curved surface area of this cone $= π \times 40 \times l = 1640 π$
$\Rightarrow l = 41 c m$
For a cone, $l = h^{2} + r^{2}$
Hence, $41 = h^{2} + 4 0^{2}$
$\Rightarrow 1681 = h^{2} + 1600$

$\Rightarrow h^{2} = 81$
$\Rightarrow h = 9 c m$

The circumference of the base of a $16$ m high solid cone is $33$ m. Find the surface area of the cone.

Find the total surface area of a right circular cone with radius $6$ cm and height $8$ cm.

The radius of a cone is $5$ cm and vertical height is $12$ cm. Find the area of the curved surface.

A $5 m$ wide cloth is used to make a conical tent of base diameter $14 m$ and height $24 m$ . Find the cost of cloth used at the rate of Rs. $25$ per metre (Use $π = 22 / 7$ )

What is the total surface area of a right circular cone of height $14 c m$ and base radius $7 c m$ ?

Two cones with same base radius $8$ cm and height $15$ cm are joined together along their bases. Find the surface area of the shape so formed.(answer to the nearest whole no.)

Find the area of canvas required for a conical tent whose height is $3.5$ m and the radius of the base is $12$ m.