Level 3 · Challenge ← Back to lesson

Surface Areas of Pyramids and Cones: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A closed regular square pyramid has total area $384\text{ cm}^2$ and base side $12$ cm. Find its perpendicular height.

Answer choices for question 1 A $10$ cm B $6$ cm C $\sqrt{136}$ cm D $8$ cm
2

A right cone has curved area $84\pi\text{ cm}^2$ and slant height $14$ cm. What sector angle forms its curved side?

Answer choices for question 2 A $\frac{540}{7}^\circ$ B $\frac{1080}{7}^\circ$ C $216^\circ$ D $\frac{2520}{7}^\circ$
3

A sector of radius $20$ cm and angle $216^\circ$ forms a right cone without overlap. Find the cone's closed surface area.

Answer choices for question 3 A $240\pi\text{ cm}^2$ B $544\pi\text{ cm}^2$ C $384\pi\text{ cm}^2$ D $256\pi\text{ cm}^2$
4

Two right cones have base radius $3$ cm. Their perpendicular heights are $4$ cm and $\sqrt{55}$ cm. How much greater is the second cone's lateral area?

Answer choices for question 4 A $9\pi\text{ cm}^2$ B $3\pi\text{ cm}^2$ C $18\pi\text{ cm}^2$ D $3\pi(\sqrt{55}-4)\text{ cm}^2$
5

A regular square pyramid has slant height $15$ cm and apex-to-base-vertex edges $17$ cm. Find its closed total surface area.

Answer choices for question 5 A $736\text{ cm}^2$ B $480\text{ cm}^2$ C $544\text{ cm}^2$ D $960\text{ cm}^2$
6

A regular hexagonal pyramid has base side $6$ cm and perpendicular height $\sqrt{73}$ cm. Find its lateral area.

Answer choices for question 6 A $18\sqrt{73}\text{ cm}^2$ B $216\text{ cm}^2$ C $180\text{ cm}^2$ D $360\text{ cm}^2$
7

A sector has radius $8$ cm and angle $270^\circ$ . It is rolled into a right cone without overlap. Which pair gives the base radius and perpendicular height?

Answer choices for question 7 A
$r=8\text{ cm}$

$h=6\text{ cm}$
B
$r=6\text{ cm}$

$h=2\sqrt7\text{ cm}$
C
$r=3\text{ cm}$

$h=\sqrt{55}\text{ cm}$
D
$r=6\text{ cm}$

$h=\sqrt{73}\text{ cm}$
8

A closed right cone has total area $180\pi\text{ cm}^2$ and radius $6$ cm. Find its perpendicular height.

Answer choices for question 8 A $24$ cm B $30$ cm C $\sqrt{612}$ cm D $\sqrt{540}$ cm
9

A regular square pyramid has base side $14$ cm and slant height $25$ cm. Find the volume using the actual perpendicular height.

Answer choices for question 9 A $\frac{4900}{3}\text{ cm}^3$ B $4704\text{ cm}^3$ C $1568\text{ cm}^3$ D $\frac{1372}{3}\text{ cm}^3$
10

A pyramid with square base side $10$ cm has two side-face altitudes of $\sqrt{61}$ cm and two of $\sqrt{41}$ cm. Find its lateral area from those face data.

Answer choices for question 10 A $10(\sqrt{61}+\sqrt{41})\text{ cm}^2$ B $20\sqrt{61}\text{ cm}^2$ C $20\sqrt{41}\text{ cm}^2$ D $5(\sqrt{61}+\sqrt{41})\text{ cm}^2$
11

A right cone has base radius $7$ cm. Its closed total surface area is three times its lateral area. Can a nondegenerate right cone satisfy this condition?

Answer choices for question 11 A Yes, with slant height $14$ cm B Yes, with slant height $7$ cm C No, because cones cannot have lateral area D No, because it would require slant height less than the base radius
12

A right-conical shell has base circumference $18\pi$ cm and curved-side area $117\pi\text{ cm}^2$ . It has no base disk. Find the sector radius and sector angle for its pattern.

Answer choices for question 12 A
$9\text{ cm}$

$360^\circ$
B
$13\text{ cm}$

$\frac{3240}{13}^\circ$
C
$13\text{ cm}$

$\frac{1620}{13}^\circ$
D
$26\text{ cm}$

$\frac{1620}{13}^\circ$

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