Question

AREA, PERIMETER & VOLUME QUESTION

QUESTION 1 in multiple choice attached.
Case A, B or C?
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QUESTION 2
What is the volume in metres of the speaker below?

Volume of a cuboid:

V = l x h x w

( SEE DIAGRAM)
The volume of the speaker is ? m3?
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QUESTION 3:
What is the missing width of the speaker below when its volume is 30,000 cm3 ?

(SEE DIAGRAM)

The missing width of the speaker is how many cms?

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QUESTION 4:
The arena has several triangular prisms that are used as advertising boards. They are to be filled with sand so they cannot easily be moved.
(SEE DIAGRAM)
What is the volume of sand needed to fill one in m3?

Answer 1

1. Case B

2. 9 cm³

3. 20 cm.

4. 4.5 m³

Explanation:

Question 1: We are required to fit a drum having volume 14,000 cm³.

We know that the volume of cylinder = πr²h, where r is the radius and h is the height. So, according to the cases:

A. Here, r = 100 mm = 10 cm, h = 300 mm = 30 cm.

So, volume of the drum = πr²h =
`\pi * 10^(2) * 30` = 9424.78 cm³.

We cannot put the given drum inside this drum.

B. Here, r = 200 mm = 20 cm, h = 30 cm.

So, volume of the drum = πr²h =
`\pi * 20^(2) * 30` = 37699.11 cm³.

C. Here, r = 32 cm, h = 250 mm = 25 cm.

So, volume of the drum = πr²h =
`\pi * 32^(2) * 25` = 80424.77 cm³.

Out of options B and C, the smallest volume is in CASE B i.e. 37699.11 cm³.

So, Case B is the correct option.

Question 2: We have the dimensions of the speaker as,

Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m

Now, Volume of a cuboid = L×W×H

Thus, volume of the speaker = 0.45 × 0.4 × 0.5 = 0.09 m³ = 9 cm³.

Question 3: We have that the volume of the speaker is 30,000 cm³.

Also, Length = 30 cm = 0.45 m, Height = 500 mm = 50 cm.

So, volume of the speaker = L×W×H

i.e. 30,000 = 30 × W × 50

i.e. W =
`(30,000)/(1500)`

i.e. W = 20 cm.

Hence, the width of the speaker is 20 cm.

Question 4: We have the dimensions as,

Base= 2 m, Length = 3 m, Height = 1.5 m

So, the volume of prism =
`(base* height)/(2) * length`

i.e. Volume =
`(2* 1.5)/(2) * 3`

i.e. Volume = 4.5

Thus, volume of the sand needed to be filled is 4.5 m³.