Surface Areas of Pyramids and Cones: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

A regular square pyramid has base side $16$ cm and perpendicular height $15$ cm. Find its slant height.

Answer choices for question 1 A $31$ cm B $\sqrt{481}$ cm C $17$ cm D $8$ cm
2

A right cone has base radius $8$ cm and perpendicular height $15$ cm. Find its closed total surface area.

Answer choices for question 2 A $200\pi\text{ cm}^2$ B $184\pi\text{ cm}^2$ C $136\pi\text{ cm}^2$ D $264\pi\text{ cm}^2$
3

A sector with radius $14$ cm and angle $180^\circ$ forms the curved side of a right cone without overlap. Find the cone's base radius.

Answer choices for question 3 A $14$ cm B $28$ cm C $3.5$ cm D $7$ cm
4

A right cone has base radius $5$ cm and slant height $18$ cm. What sector angle forms its curved side?

Answer choices for question 4 A $50^\circ$ B $100^\circ$ C $180^\circ$ D $324^\circ$
5

A regular square pyramid has lateral area $160\text{ cm}^2$ and base side $10$ cm. Find its slant height.

Answer choices for question 5 A $16$ cm B $8$ cm C $4$ cm D $\sqrt{89}$ cm
6

A regular hexagonal pyramid has base side $4$ cm and slant height $6$ cm. Find its closed surface area exactly.

Answer choices for question 6 A $(144+24\sqrt3)\text{ cm}^2$ B $(72+16\pi)\text{ cm}^2$ C $(72+48\sqrt3)\text{ cm}^2$ D $(72+24\sqrt3)\text{ cm}^2$
7

A closed right cone has total area $96\pi\text{ cm}^2$ and curved-side area $60\pi\text{ cm}^2$ . Find its radius.

Answer choices for question 7 A $6$ cm B $36$ cm C $10$ cm D $\sqrt{96}$ cm
8

An ideal right-conical canopy has rim diameter $8$ m and perpendicular height $3$ m. It includes the curved covering and no floor disk. Find the covering area.

Answer choices for question 8 A $36\pi\text{ m}^2$ B $12\pi\text{ m}^2$ C $20\pi\text{ m}^2$ D $40\pi\text{ m}^2$
9

A right cone has slant height $13$ cm and base radius $12$ cm. Find its perpendicular height.

Answer choices for question 9 A $25$ cm B $\sqrt{313}$ cm C $1$ cm D $5$ cm
10

A pyramid has a $6$ cm by $8$ cm rectangular base. Each face based on a $6$ cm edge has altitude $5$ cm, and each face based on an $8$ cm edge has altitude $\sqrt{18}$ cm. Find its lateral area.

Answer choices for question 10 A $70\text{ cm}^2$ B $(30+8\sqrt{18})\text{ cm}^2$ C $(15+4\sqrt{18})\text{ cm}^2$ D $(48+8\sqrt{18})\text{ cm}^2$
11

A sector of radius $10$ cm has selected arc length $12\pi$ cm. It forms a right cone's curved side without overlap. Find the perpendicular cone height.

Answer choices for question 11 A $6$ cm B $10$ cm C $8$ cm D $\sqrt{136}$ cm
12

A regular square pyramid has base side $9$ cm and slant height $7.5$ cm. All four side faces are present but the square base is absent. Find the material area.

Answer choices for question 12 A $135\text{ cm}^2$ B $216\text{ cm}^2$ C $270\text{ cm}^2$ D $67.5\text{ cm}^2$