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if the slant height (l) of a cone is equ...

if the slant height (l) of a cone is equal to the square root of the sum of the squares of radius (r) and height (h) then,

A

`l=r^(2)+h^(2)`

B

`l=sqrt(r^(2)+h^(2))`

C

`l^(2)=sqrt(r^(2)+h^(2))`

D

`r^(2)-h^(2)=l^(2)`.

Text Solution

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The correct Answer is:
B
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The slant height (l) of a cone is the square root of the sum of the squares of its radius (r) and its vertical height (h). If for a cone, l=17cm and r=15 cm, then find h.

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Knowledge Check

  • If the sum of the square of p and twice of q is equal to the square root of the sum of the square of r and s, write a formula with p as the subject.

    A
    ` p = sqrt(2p - sqrt(r^(2)+s^(2)))`
    B
    ` p = sqrt(r^(2) +s^(2) - 2q) `
    C
    ` p = sqrt(2q- r^(2) - s^(2))`
    D
    ` p = sqrt(1-k^(2))`

  • If the sum of the square of p and twice of q is equal to the square root of the sum of the square of r and s, wirte a formula wth p as the subject.

    A
    `p=sqrt(2q-sqrt(r^(2)+s^(2)))`
    B
    `p=sqrt(r^(2)+s^(2)-2q)`
    C
    `p=sqrt(2q-r^(2)-s^(2))`
    D
    `p=sqrt(1-k^(2))`

  • Assertion (A) : If the height of the cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm. Reason (R) : If r be the radius of the cone and h be the height of the cone, then slant height = sqrt((h^(2) + r^(2))) .

    A
    Both A and R are true and R is the correct explanation of A.
    B
    Both A and R are true and R is not the correct explanation of A.
    C
    A is true but R is false
    D
    A is false but R is true

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