The radius of the base and height of a right circular cone are in the ratio of 5 : 12. If its volume is 2512 {cm}³, find its curved surface area and total surface area. (Use π = 3.14)

Correct Answer is : 816.4 cm2{cm}²cm2; 1130.4 cm2{cm}²cm2

Correct Answer is : 816.4 cm2{cm}²cm2; 1130.4 cm2{cm}²cm2

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Volumes Practice Test 4

Question : 7 of 16

Marks: +1, -0

\mathrm{cm}^3

Solution:

Concept:

For a right circular cone, volume, curved surface area, and total surface area are found using its radius, height, and slant height.

Explanation:

Let

r=5x\ \mathrm{cm}

and

h=12x\ \mathrm{cm}

, since

r:h=5:12

Volume of cone

=\frac{1}{3}\pi r^2h=2512

So,

\frac{1}{3}\times 3.14\times (5x)^2\times 12x=2512

\Rightarrow 3.14\times 100x^3=2512

\Rightarrow x^3=\frac{2512}{314}=8

\Rightarrow x=2

Thus,

r=5\times 2=10\ \mathrm{cm}

and

h=12\times 2=24\ \mathrm{cm}

Slant height

l=\sqrt{r^2+h^2}=\sqrt{10^2+24^2}=\sqrt{676}=26\ \mathrm{cm}

Curved surface area

=\pi rl=3.14\times 10\times 26=816.4\ \mathrm{cm}^2

Total surface area

=\pi r(l+r)=3.14\times 10\times (26+10)=1130.4\ \mathrm{cm}^2

Answer:

Curved surface area

=816.4\ \mathrm{cm}^2

and total surface area

=1130.4\ \mathrm{cm}^2

So the correct option is A.

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