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Volumes Practice Test 3

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Question : 2 of 40

Marks: +1, -0

If a right circular cone of height 24 cm has a volume of 1232

\mathrm{cm}^3

, then find its curved surface area.

220 $\mathrm{cm}^2$
330 $\mathrm{cm}^2$
440 $\mathrm{cm}^2$
550 $\mathrm{cm}^2$

Solution:

Concept:

The volume of a cone links its radius and height, and its curved surface area uses the slant height.

Explanation:

Volume of cone is

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

.

Given

h=24\ \mathrm{cm}

and volume

=1232\ \mathrm{cm}^3

, using

\pi=\frac{22}{7}

:

\frac{1}{3}\times \frac{22}{7}\times r^2 \times 24 = 1232

r^2=\frac{1232\times 7}{22\times 8}=49

r=7\ \mathrm{cm}

Slant height is

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

.

l=\sqrt{7^2+24^2}=\sqrt{625}=25\ \mathrm{cm}

Curved surface area

=\pi r l=\frac{22}{7}\times 7 \times 25

=22\times 25=550\ \mathrm{cm}^2

Answer:

550\ \mathrm{cm}^2

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