Prisms and Cylinders: Practice Level 3 | Geometry

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A right circular cylinder has volume $162\pi$ cubic cm and curved-side area $54\pi$ square cm. What is its radius?

Answer choices for question 1 A $3$ cm B $9$ cm C $12$ cm D $6$ cm
2

An ideal right cylindrical boundary includes its curved side and one base. Its volume is $120\pi$ cubic cm and its curved-side area is $60\pi$ square cm. What total boundary area is included?

Answer choices for question 2 A $60\pi$ square cm B $76\pi$ square cm C $92\pi$ square cm D $120\pi$ square cm
3

A closed right triangular prism has right triangular bases with sides $9$ , $12$ , and $15$ cm. Its total surface area is $396$ square cm. What is its volume?

Answer choices for question 3 A $594$ cubic cm B $864$ cubic cm C $432$ cubic cm D $648$ cubic cm
4

A rectangular container has inside base dimensions $8$ cm by $5$ cm and capacity $1.2$ liters. What is its inside height? Use $1$ liter as $1{,}000$ cubic cm.

Answer choices for question 4 A $30$ cm B $0.03$ cm C $3$ cm D $15$ cm
5

An oblique prism has base area $14$ square cm. In a perpendicular side view, a joining edge is the hypotenuse of a right triangle with length $17$ cm and horizontal offset $8$ cm. What is the prism's volume?

Answer choices for question 5 A $238$ cubic cm B $112$ cubic cm C $210$ cubic cm D $350$ cubic cm
6

A closed right circular cylinder has radius $\sqrt{10}$ cm and height $9$ cm. What is its exact total surface area?

Answer choices for question 6 A $90\pi$ square cm B $(20+9\sqrt{10})\pi$ square cm C $(10+18\sqrt{10})\pi$ square cm D $(20+18\sqrt{10})\pi$ square cm
7

Two ordinary solids lie between the same parallel planes. Every base-parallel section of the first is a square, and every corresponding section of the second is a disk of equal area. What does Cavalieri establish?

Answer choices for question 7 A Their volumes are equal B Their boundaries have equal areas C The square and disk have equal perimeters D The solids are congruent
8

A closed right circular cylinder has base circumference $14\pi$ cm and total surface area $196\pi$ square cm. What is its volume?

Answer choices for question 8 A $686\pi$ cubic cm B $343\pi$ cubic cm C $196\pi$ cubic cm D $49\pi$ cubic cm
9

A closed right prism has height $10$ cm, lateral area $420$ square cm, and total surface area $588$ square cm. What is its volume?

Answer choices for question 9 A $1680$ cubic cm B $4200$ cubic cm C $5880$ cubic cm D $840$ cubic cm
10

A right circular cylinder has volume $375\pi$ cubic cm and height $15$ cm. What is its curved-side area?

Answer choices for question 10 A $750\pi$ square cm B $75\pi$ square cm C $150\pi$ square cm D $200\pi$ square cm
11

A closed right prism has base area $35$ square cm, base perimeter $24$ cm, and surface area $286$ square cm. One entire base is removed, leaving all side faces and the other base. What is the remaining boundary area?

Answer choices for question 11 A $216$ square cm B $251$ square cm C $321$ square cm D $181$ square cm
12

A closed right rectangular prism has height $6$ cm. Its base sides are $x$ cm and $x+4$ cm, where $x$ is positive. The prism volume is $270$ cubic cm. What is its total surface area?

Answer choices for question 12 A $258$ square cm B $168$ square cm C $213$ square cm D $540$ square cm