Surface Areas of Pyramids and Cones: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

Which length is the slant height of a regular pyramid?

Answer choices for question 1 A The distance from the apex perpendicular to the base plane B The altitude of a triangular side face from the apex to its base edge C The distance from the apex to a base vertex D The base perimeter
2

A regular pyramid has base perimeter $28$ cm and slant height $6$ cm. Find its lateral area.

Answer choices for question 2 A $168\text{ cm}^2$ B $34\text{ cm}^2$ C $42\text{ cm}^2$ D $84\text{ cm}^2$
3

A regular square pyramid has base side $4$ cm and slant height $7$ cm. Find its closed total surface area.

Answer choices for question 3 A $72\text{ cm}^2$ B $56\text{ cm}^2$ C $88\text{ cm}^2$ D $44\text{ cm}^2$
4

When a right cone's curved side is unfolded, which cone length becomes the sector radius?

Answer choices for question 4 A The base diameter B The perpendicular height C The slant height D The base radius
5

A right cone has base radius $6$ cm. What length must the selected arc of its sector pattern have?

Answer choices for question 5 A $6\pi$ cm B $36\pi$ cm C $12\pi$ cm D $12$ cm
6

A right cone has radius $4$ cm and slant height $11$ cm. Find its lateral area.

Answer choices for question 6 A $44\pi\text{ cm}^2$ B $16\pi\text{ cm}^2$ C $60\pi\text{ cm}^2$ D $88\pi\text{ cm}^2$
7

A closed right cone has radius $2$ cm and slant height $7$ cm. Find its total surface area.

Answer choices for question 7 A $14\pi\text{ cm}^2$ B $22\pi\text{ cm}^2$ C $28\pi\text{ cm}^2$ D $18\pi\text{ cm}^2$
8

A pyramid's triangular side faces have different altitudes. Which method is justified for its lateral area?

Answer choices for question 8 A Multiply half the base perimeter by the shortest face altitude B Add each triangle area using its own base and altitude C Multiply half the base perimeter by the perpendicular solid height D Multiply the base area by the perpendicular height
9

A right cone has radius $9$ cm and slant height $15$ cm. Its base disk is removed while the curved side is kept. How much surface area is removed?

Answer choices for question 9 A $81\pi\text{ cm}^2$ B $135\pi\text{ cm}^2$ C $216\pi\text{ cm}^2$ D $18\pi\text{ cm}^2$
10

Which statement correctly describes a nondegenerate right circular cone?

Answer choices for question 10 A The slant height and radius are legs whose hypotenuse is the perpendicular height B The perpendicular height always equals the slant height C The perpendicular height and radius are legs of a right triangle whose hypotenuse is the slant height D The base diameter is always the slant height
11

A regular pyramid has lateral area $63\text{ cm}^2$ and base area $20\text{ cm}^2$ . Find its closed total surface area.

Answer choices for question 11 A $103\text{ cm}^2$ B $83\text{ cm}^2$ C $43\text{ cm}^2$ D $1260\text{ cm}^2$
12

An ideal right-conical shell has its entire curved side and no base disk. Which expression gives its single-layer material area?

Answer choices for question 12 A $\pi r\ell+\pi r^2$ B $2\pi r\ell$ C $\tfrac13\pi r^2h$ D $\pi r\ell$