# A cone of height 2.8 cm has a lateral surface area 23.10 cm^2.what is the radius of the base.please solve it urgently.please .please

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by anudeepd2

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by anudeepd2

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Lateral surface area is given by π R L L = lateral length or lateral height

L² = R² + H² H = height of cone

L² = R² + 2.8² ----- equation 1

23.10 = 3.14 * R * L

R L = 7.353 cm²

L = 7.353 / R

Substitute in equation 1

7.353² /R² = R² + 2.8²

R^4 + 7.84 R² - 54.066 = 0

Δ = 277.73

R² = 4.412

__R = 2.1 cm__

L = 3.5 cm

L² = R² + H² H = height of cone

L² = R² + 2.8² ----- equation 1

23.10 = 3.14 * R * L

R L = 7.353 cm²

L = 7.353 / R

Substitute in equation 1

7.353² /R² = R² + 2.8²

R^4 + 7.84 R² - 54.066 = 0

Δ = 277.73

R² = 4.412

L = 3.5 cm

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Lateral surface area is given by πrl l = lateral height

l² = r² + h² h = height of cone = 2.8 cm

l = √ (r² + 2.8²) ----- i

23.10 = 3.14 × r × l

rl = 7.353 cm²

l = 7.353 / r

So

7.353/r = √(r² + 2.8²)

7.353² /r² = r² + 2.8²

r⁴ + 7.84r² - 54.066 = 0

solving r

r = 2.1003 cm

l² = r² + h² h = height of cone = 2.8 cm

l = √ (r² + 2.8²) ----- i

23.10 = 3.14 × r × l

rl = 7.353 cm²

l = 7.353 / r

So

7.353/r = √(r² + 2.8²)

7.353² /r² = r² + 2.8²

r⁴ + 7.84r² - 54.066 = 0

solving r