The slant height of a conical mountain is 2.5 km. The area of the base of the mountain is \frac{49}{100} \pi r sq. km. Then the height of the mountain is:

Mensuration Practice Test 10

Question : 32 of 40

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The slant height of a conical mountain is 2.5 km. The area of the base of the mountain is

{49}/{100} π

r sq. km. Then the height of the mountain is:

Solution:

Slant height of the conical mountain = 2.5 km.
Area =

{49}/{100}

π sq. km
πrl =

{49}/{100}π

r × 2.5 =

{49}/{100}

r =

{49}/{100} × {10}/{25}

r = 0.196 km
Height =

√{l^2-r^2}

√{(2.5)^2-(0.196)^2}

√{(6.25)-(0.038)}

√{6.212}

= 2.4 km

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