Measurement, NAPX-F4-CA21

Question

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Worked Solution

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Variant 0

DifficultyLevel

631

Question

A cube has a side length of 8 cm.

Two smaller cubes of side length 4 cm are attached to the larger cube as shown in the diagram below.



Including the base, what is the surface area of the new object?

Worked Solution

One strategy:

Calculate the surface area (S.A.) of each object then deduct the faces not showing.

S.A. (large cube) = 6 × 8 × 8 = 384 cm2^2

S.A. (small cube) = 6 × 4 × 4 = 96 cm2^2

S.A. (sides not showing) = 6 × (4 × 4) = 96 cm2^2

∴\therefore Total S.A.
= 384 + (2 × 96) − 96
= 480 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cube has a side length of 8 cm. Two smaller cubes of side length 4 cm are attached to the larger cube as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2017/01/naplan-2013-21mc-300x207.png 240 indent vpad
Including the base, what is the surface area of the new object?
workedSolution
One strategy: Calculate the surface area (S.A.) of each object then deduct the faces not showing. S.A. (large cube) = 6 × 8 × 8 = 384 cm$^2$ S.A. (small cube) = 6 × 4 × 4 = 96 cm$^2$ S.A. (sides not showing) = 6 × (4 × 4) = 96 cm$^2$ sm_nogap $\therefore$ Total S.A.
>>|| |-| |= 384 + (2 × 96) − 96| |= {{{correctAnswer}}}|
correctAnswer
480 cm$^2$

Answers

Is Correct?Answer
✓

480 cm2^2

x

496 cm2^2

x

512 cm2^2

x

576 cm2^2

Variant 1

DifficultyLevel

630

Question

A cube has a side length of 6 cm.

Four smaller cubes of side length 3 cm are attached to the larger cube as shown in the diagram below.



Including the base, what is the surface area of the new object?

Worked Solution

One strategy:

Calculate the surface area (S.A.) of each object then deduct the faces not showing.

S.A. (large cube) = 6 × 6 × 6 = 216 cm2^2

S.A. (small cube) = 6 × 3 × 3 = 54 cm2^2

S.A. (sides not showing) = 12 × (3 × 3) = 108 cm2^2

∴\therefore Total S.A.
= 216 + (4 × 54) − 108
= 324 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cube has a side length of 6 cm. Four smaller cubes of side length 3 cm are attached to the larger cube as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA21_v1.svg 240 indent vpad
Including the base, what is the surface area of the new object?
workedSolution
One strategy: Calculate the surface area (S.A.) of each object then deduct the faces not showing. S.A. (large cube) = 6 × 6 × 6 = 216 cm$^2$ S.A. (small cube) = 6 × 3 × 3 = 54 cm$^2$ S.A. (sides not showing) = 12 × (3 × 3) = 108 cm$^2$ sm_nogap $\therefore$ Total S.A.
>>|| |-| |= 216 + (4 × 54) − 108| |= {{{correctAnswer}}}|
correctAnswer
324 cm$^2$

Answers

Is Correct?Answer
x

72 cm2^2

✓

324 cm2^2

x

360 cm2^2

x

416 cm2^2

Variant 2

DifficultyLevel

629

Question

A cube has a side length of 20 cm.

Two smaller cubes of side length 10 cm are attached to the larger cube as shown in the diagram below.



Including the base, what is the surface area of the new object?

Worked Solution

One strategy:

Calculate the surface area (S.A.) of each object then deduct the faces not showing.

S.A. (large cube) = 6 × 20 × 20 = 2400 cm2^2

S.A. (small cube) = 6 × 10 × 10 = 600 cm2^2

S.A. (sides not showing) = 6 × (10 × 10) = 600 cm2^2

∴\therefore Total S.A.
= 2400 + (2 × 600) − 600
= 3000 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cube has a side length of 20 cm. Two smaller cubes of side length 10 cm are attached to the larger cube as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA21_v2.svg 240 indent vpad
Including the base, what is the surface area of the new object?
workedSolution
One strategy: Calculate the surface area (S.A.) of each object then deduct the faces not showing. S.A. (large cube) = 6 × 20 × 20 = 2400 cm$^2$ S.A. (small cube) = 6 × 10 × 10 = 600 cm$^2$ S.A. (sides not showing) = 6 × (10 × 10) = 600 cm$^2$ sm_nogap $\therefore$ Total S.A.
>>|| |-| |= 2400 + (2 × 600) − 600| |= {{{correctAnswer}}}|
correctAnswer
3000 cm$^2$

Answers

Is Correct?Answer
✓

3000 cm2^2

x

3200 cm2^2

x

3600 cm2^2

x

10 000 cm2^2

Variant 3

DifficultyLevel

628

Question

A cube has a side length of 10 cm.

Four smaller cubes of side length 5 cm are attached to the larger cube as shown in the diagram below.



Including the base, what is the surface area of the new object?

Worked Solution

One strategy:

Calculate the surface area (S.A.) of each object then deduct the faces not showing.

S.A. (large cube) = 6 × 10 × 10 = 600 cm2^2

S.A. (small cube) = 6 × 5 × 5 = 150 cm2^2

S.A. (sides not showing) = 12 × (5 × 5) = 300 cm2^2

∴\therefore Total S.A.
= 600 + (4 × 150) − 300
= 900 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cube has a side length of 10 cm. Four smaller cubes of side length 5 cm are attached to the larger cube as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA21_v3.svg 240 indent vpad
Including the base, what is the surface area of the new object?
workedSolution
One strategy: Calculate the surface area (S.A.) of each object then deduct the faces not showing. S.A. (large cube) = 6 × 10 × 10 = 600 cm$^2$ S.A. (small cube) = 6 × 5 × 5 = 150 cm$^2$ S.A. (sides not showing) = 12 × (5 × 5) = 300 cm$^2$ sm_nogap $\therefore$ Total S.A.
>>|| |-| |= 600 + (4 × 150) − 300| |= {{{correctAnswer}}}|
correctAnswer
900 cm$^2$

Answers

Is Correct?Answer
x

600 cm2^2

x

750 cm2^2

✓

900 cm2^2

x

1500 cm2^2

Variant 4

DifficultyLevel

637

Question

A cube has a side length of 14 cm.

Two smaller cubes of side length 7 cm are attached to the larger cube as shown in the diagram below.



Including the base, what is the surface area of the new object?

Worked Solution

One strategy:

Calculate the surface area (S.A.) of each object then deduct the faces not showing.

S.A. (large cube) = 6 × 14 × 14 = 1176 cm2^2

S.A. (small cube) = 6 × 7 × 7 = 294 cm2^2

S.A. (sides not showing) = 4 × (7 × 7) = 196 cm2^2

∴\therefore Total S.A.
= 1176 + (2 × 294) − 196
= 1568 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cube has a side length of 14 cm. Two smaller cubes of side length 7 cm are attached to the larger cube as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA21_v4.svg 240 indent vpad
Including the base, what is the surface area of the new object?
workedSolution
One strategy: Calculate the surface area (S.A.) of each object then deduct the faces not showing. S.A. (large cube) = 6 × 14 × 14 = 1176 cm$^2$ S.A. (small cube) = 6 × 7 × 7 = 294 cm$^2$ S.A. (sides not showing) = 4 × (7 × 7) = 196 cm$^2$ sm_nogap $\therefore$ Total S.A.
>>|| |-| |= 1176 + (2 × 294) − 196| |= {{{correctAnswer}}}|
correctAnswer
1568 cm$^2$

Answers

Is Correct?Answer
x

3430 cm2^2

x

1669 cm2^2

✓

1568 cm2^2

x

1470 cm2^2

Variant 5

DifficultyLevel

636

Question

A cube has a side length of 8 cm.

Three smaller cubes of side length 4 cm are attached to the larger cube as shown in the diagram below.



Including the base, what is the surface area of the new object?

Worked Solution

One strategy:

Calculate the surface area (S.A.) of each object then deduct the faces not showing.

S.A. (large cube) = 6 × 8 × 8 = 384 cm2^2

S.A. (small cube) = 6 × 4 × 4 = 96 cm2^2

S.A. (sides not showing) = 6 × (4 × 4) = 96 cm2^2

∴\therefore Total S.A.
= 384 + (3 × 96) − 96
= 576 cm2^2

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cube has a side length of 8 cm. Three smaller cubes of side length 4 cm are attached to the larger cube as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA21_v5.svg 240 indent vpad
Including the base, what is the surface area of the new object?
workedSolution
One strategy: Calculate the surface area (S.A.) of each object then deduct the faces not showing. S.A. (large cube) = 6 × 8 × 8 = 384 cm$^2$ S.A. (small cube) = 6 × 4 × 4 = 96 cm$^2$ S.A. (sides not showing) = 6 × (4 × 4) = 96 cm$^2$ sm_nogap $\therefore$ Total S.A.
>>|| |-| |= 384 + (3 × 96) − 96| |= {{{correctAnswer}}}|
correctAnswer
576 cm$^2$

Answers

Is Correct?Answer
✓

576 cm2^2

x

624 cm2^2

x

672 cm2^2

x

704 cm2^2

Tags

  • ms_ca