Question

There are 100 students in class IX of a school. Mathematics teacher asks all the students to Prepare a cylindrical container with base at the bottom but open at the top , using cardboard. Each student has to make one container of diameter 8.4 cm and height 11.2 cm. The cost of the Cardboard is Rs. 10 per 100 cm2. Find the amount spent by the teacher for the purchase of the Cardboard.

Answer 1

Given :

• Number of students in class IX = 100

Cylindrical container is opened at the top

• Height of cylinder (h) = 11.2 cm

Diameter of cylinder = 8.4cm

• Radius of cylinder (r) = Diameter/2 = 4.2cm

To find :

The amount spent by the teacher for the purchase of the Cardboard.

Solution :

Total surface area of cylinder is given as :

• 2πrh + 2 × area of two circles

★ But cylindrical container is opened at the top

→ 2πrh + πr²

→ πr(2h + r)

• Put the value of height and radius

→ 22/7 × 4.2(2 × 11.2 + 4.2)

→ 22 × 0.6(22.4 + 4.2)

→ 13.2 × 26.6

→ 351.12 cm²

★ Area of cardboard if 100 students made such cylindrical container

• 351.12 × 100 = 35112cm²

★ Now, the cost of the Cardboard is Rs.10 per 100 cm².

★ Cost of 1cm² of the cardboard = 100/10 = Rs.10

→ Cost of 351.12 cm² of the cardboard

→ 35112 × 10 = Rs.351120

•°• The amount spent by the teacher for the purchase of the cardboard is Rs.351120

Answer 2

Answer:

Given :-

• There are 100 students in a class IX of a school.
• One container of diameter is 8.4 cm and height is 11.2 cm.
• The cost of the Cardboard is Rs 10 per 100 cm².

To Find :-

• What is the amount spent by the teacher for the purchase of the Cardboard.

Solution :-

First, we have to find the radius of the cylinder :

As we know that :

❖ Radius = Diameter/2 ❖

Given :

• Diameter = 8.4 cm

↦ Radius = 8.4/2

↦ Radius = 84/10 × 2

↦ Radius = 84/20

↦ Radius = 21/5

➦ Radius = 4.2 cm

Then, we have to find the total surface area of open cylinder :

As we know that :

★ T.S.A of Cylinder = 2πr(h + r) ★

But, as it is opened at the top of a cylindrical container. So the formula will be :

✯ Open Cylinder = πr(2h + r) ✯

Given :

• Radius = 4.2 cm
• Height = 11.2 cm

According to the question by using the formula we get,

↦ 22/7 × 4.2(2(11.2) + 4.2)

↦ 22/7 × 4.2(22.4 + 4.2)

↦ 22/7 × 4.2(26.6)

↦ 22/7 × 111.72

➠ 351.12 cm².

Now, 100 students is making this cardboard by each student :

↦ 351.12 × 100

↦ 35112/100 × 100

↦ 35112/1

➦ 35112 cm²

Again, we have to find the amount spent by the teacher for the purchase of the Cardboard,

➤ It is given that the cost of the Cardboard is Rs 10 per 100 cm²,

To find this we have to use unitary method,

If, cost of 1 cm² of cardboard is Rs 10.

Then, 35112 cm² of cardboard will cost,

↦ Rs 10 × 35112

➠ Rs 351120

∴ The amount spent by the teacher for the purchase of the Cardboard is Rs 351120 .

__________________________

IMPORTANT FORMULA RELATED TO RIGHT CIRCULAR CYLINDER :

✪ C.S.A of Cylinder = 2πrh

✪ T.S.A of Cylinder = 2πr(h + r)

✪ Volume of Cylinder = πr²h

✪ Diameter = 2 × r

✪ Perimeter of Cylinder = 2πr

✪ Base Area of Cylinder = πr²

where,

• r = Radius
• h = Height