Question

AREA, PERIMETER & VOLUME QUESTION

Answer 1

Answer:

1. Case B

2.  9 cm³

3. 20 cm.

4. 4.5 m³

Step-by-step 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 = $\pi \times 10^{2} \times 30$ = 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 = $\pi \times 20^{2} \times 30$ = 37699.11 cm³.

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

So, volume of the drum =  πr²h = $\pi \times 32^{2} \times 25$ = 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 = $\frac{30,000}{1500}$

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 = $\frac{base\times height}{2} \times length$

i.e. Volume =  $\frac{2\times 1.5}{2} \times 3$

i.e. Volume = 4.5

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