Surface Areas and Volumes Final Assessment

Core Concepts

Question 1mcq

A hemisphere of volume

72\pi\text{ cm}^3

is attached to a cylinder of volume

120\pi\text{ cm}^3

. Find total volume.

A.

120\pi\text{ cm}^3

B.

192\pi\text{ cm}^3

C.

48\pi\text{ cm}^3

D.

8640\pi\text{ cm}^3

Question 2mcq

In a second review item, a cuboid of volume

1000\text{ cm}^3

has a cylindrical hole of volume

120\text{ cm}^3

removed. What is the remaining volume?

A.

880\text{ cm}^3

B.

1120\text{ cm}^3

C.

120000\text{ cm}^3

D.

1000\text{ cm}^3

Question 3mcq

In a second review item, a cylindrical pipe is attached to a cuboid tank. Which pair of formulas may be needed for volume?

A.

2\pi r

and

lb

B.

4\pi r^2

and

l+b+h

C.

\frac13\pi r^2h

and

a^2

D.

\pi r^2h

and

lbh

Question 4mcq

In a second review item, a cone is placed on a cylinder of the same radius. Which surface is usually hidden at the joint?

A.The cylinder curved surface

B.The top point of the cone

C.The circular base where cone and cylinder meet

D.The cone curved surface

Question 5mcq

In a second review item, a hemispherical dome sits on a cylinder. For exposed outer surface area, which areas are added?

A.Only circular base area

B.CSA of cylinder + CSA of hemisphere

C.TSA of cylinder + TSA of sphere

D.Volume of cylinder + area of hemisphere

Question 6mcq

In a second review item, what is the volume of a sphere of radius

3

cm?

A.

36\pi\text{ cm}^3

B.

12\pi\text{ cm}^3

C.

9\pi\text{ cm}^3

D.

18\pi\text{ cm}^3

Skill Practice

Question 7mcq

In a second review item, a cuboid

10\times8\times5

cm is joined to a cube of side

5

cm. What is the total volume?

A.

400\text{ cm}^3

B.

125\text{ cm}^3

C.

650\text{ cm}^3

D.

525\text{ cm}^3

Question 8mcq

How many millilitres are there in

3.75

litres?

A.

37.5

mL

B.

37500

mL

C.

3750

mL

D.

375

mL

Question 9mcq

In a second review item, a cylindrical tank is open at the top. To find metal sheet needed, which surface area is counted?

A.Only circumference

B.Curved surface area plus one circular base

C.Curved surface area plus two bases

D.Only volume

Question 10mcq

In a second review item, two cubes are glued face-to-face. Which surfaces should not be counted in exposed surface area?

A.The two glued internal faces

B.All outer faces

C.Only top faces

D.No faces are hidden

Question 11mcq

For a cone with radius

5

cm and height

12

cm, what is the slant height?

A.

17

cm

B.

7

cm

C.

60

cm

D.

13

cm

Question 12mcq

In a second review item, a student uses

\pi r^2h

to find the amount of paint for the outside of a cylinder. What is wrong?

A.Paint needs litres only

B.Radius should never be used

C.

\pi r^2h

is volume, not surface area

D.It is the correct formula for paint

Application and Reasoning

Question 13mcq

In a second review item, which approach best matches the skill: identify component solids in a combination?

A.Ignore units and shape features

B.Break the solid into known parts and decide whether surface area or volume is needed.

C.Use volume formula for every problem

D.Count hidden shared surfaces as exposed

Question 14mcq

In a second review item, which approach best matches the skill: distinguish tsa, csa and exposed area?

A.Break the solid into known parts and decide whether surface area or volume is needed.

B.Use volume formula for every problem

C.Count hidden shared surfaces as exposed

D.Ignore units and shape features

Question 15mcq

In a second review item, a solid consists of a cylinder of volume

300\text{ cm}^3

and a cone of volume

100\text{ cm}^3

joined together. What is the total volume?

A.

200\text{ cm}^3

B.

30000\text{ cm}^3

C.

100\text{ cm}^3

D.

400\text{ cm}^3

Question 16mcq

In a second review item, which approach best matches the skill: subtract volumes for hollow or removed parts?

A.Count hidden shared surfaces as exposed

B.Ignore units and shape features

C.Break the solid into known parts and decide whether surface area or volume is needed.

D.Use volume formula for every problem

Question 17mcq

In a second review item, which approach best matches the skill: solve cylinder-cuboid combinations?

A.Ignore units and shape features

B.Break the solid into known parts and decide whether surface area or volume is needed.

C.Use volume formula for every problem

D.Count hidden shared surfaces as exposed

Question 18mcq

In a second review item, which approach best matches the skill: solve cone-cylinder combinations?

A.Break the solid into known parts and decide whether surface area or volume is needed.

B.Use volume formula for every problem

C.Count hidden shared surfaces as exposed

D.Ignore units and shape features

Mixed Challenge

Question 19mcq

In a second review item, which approach best matches the skill: solve hemisphere-cylinder combinations?

A.Use volume formula for every problem

B.Count hidden shared surfaces as exposed

C.Ignore units and shape features

D.Break the solid into known parts and decide whether surface area or volume is needed.

Question 20mcq

In a second review item, which approach best matches the skill: solve sphere-related combinations?

A.Count hidden shared surfaces as exposed

B.Ignore units and shape features

C.Break the solid into known parts and decide whether surface area or volume is needed.

D.Use volume formula for every problem

Question 21mcq

In a second review item, which approach best matches the skill: solve cube-cuboid combinations?

A.Ignore units and shape features

B.Break the solid into known parts and decide whether surface area or volume is needed.

C.Use volume formula for every problem

D.Count hidden shared surfaces as exposed

Question 22mcq

In a second review item, convert

2500\text{ cm}^3

into litres.

A.

2.5

L

B.

25

L

C.

0.25

L

D.

250

L

Question 23mcq

In a second review item, which approach best matches the skill: solve container and material problems?

A.Use volume formula for every problem

B.Count hidden shared surfaces as exposed

C.Ignore units and shape features

D.Break the solid into known parts and decide whether surface area or volume is needed.

Question 24mcq

In a second review item, which approach best matches the skill: identify hidden and shared surfaces?

A.Count hidden shared surfaces as exposed

B.Ignore units and shape features

C.Break the solid into known parts and decide whether surface area or volume is needed.

D.Use volume formula for every problem