Question

Find the height $h$ of a cone if area $A = 1507.9645 cm$ and Curved Surface Area $CS A = 706.8583 cm$ .

Answer

Problem has no solutions.

Explanation

STEP 1: find base area $A B$

To find base area $A B$ use formula:

A = A B + CS A

After substituting $A = 1507.9645 cm$ and $CS A = 706.8583 cm$ we have:

1507.9645 cm = A B + 706.8583 cm

1507.9645 cm = A B + 706.8583 cm

1 A B = 1507.9645 cm - 706.8583 cm

1 A B = 801.1061 cm

A B = 801.1061 cm

STEP 2: find radius $r$

To find radius $r$ use formula:

After substituting $A B = 801.1061 cm$ we have:

A B = r^{2} \cdot π

r^{2} \cdot π = 801.1061 cm

r = \frac{801.1061 cm}{π}

r \approx 15.9687

STEP 3: find slant height $l$

To find slant height $l$ use formula:

CS A = l \cdot r \cdot π

After substituting $CS A = 706.8583 cm$ and $r = 15.9687 cm^{0}$ we have:

706.8583 cm = 15.9687 \cdot l \cdot π

l = \frac{706.8583 cm}{15.9687 π}

l \approx 14.09 cm

STEP 4: find side $h$

To find side $h$ use Pythagorean Theorem:

r^{2} + h^{2} = l^{2}

After substituting $r = 15.9687 cm^{0}$ and $l = 14.09 cm$ we have:

15.9687 + h^{2} = (14.09 cm)^{2}

h^{2} = (14.09 cm)^{2} - 15.9687

h^{2} = 198.5289 cm^{2} - 254.9994

h^{2} = - 56.4705 cm^{2}

This equation has no solution $⟹$ The problem has no solution.

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