Mensuration Made Great : With Word Problems For Class 8th,9th,10th[15]

Q.1) A tank of dimensions 12m * 8m * 5m is to be made of a metal sheet. It is open from the top. If the metal sheet is 4m wide, find the cost of the metal sheet required at the rate of Rs. 11.50 per meter.

SOLUTION:

Given:
Length of the room = L = 12m
Breadth of the room = B = 8m
Height of the room = H = 5m

Area of the metal sheet required = Area of the four walls + Area of the base
= 2 ( L + B ) * H + L * B
= 2 ( 12m + 8m ) * 5m + 12m * 8m
= 20m * 10m + 96m²
= 296m²

Width of the metal sheet = 4m [ Given ]
Length of the metal sheet = Area of the sheet / its width = 296 / 4 = 74m

Cost of the metal sheet = Rs. ( 74 * 11.50 ) = Rs. 851

Hence, the cost of the metal sheet required to make the tank is Rs. 851.
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Q.2) Find the lateral surface area of a right circular cylinder of height 14cm and radius 8cm.

SOLUTION:

Given:
Radius of the cylinder = 8cm
Height of the cylinder = 14cm

Lateral surface area of the cylinder = 2rh = 2 * 22 / 7 * 8 * 14 = 704cm²

Hence, lateral surface area of the right circular cylinder is 704cm².
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Q.3) Find the total surface area of a right circular cylinder whose diameter is 14cm and height is 10cm.

SOLUTION:

Given:
Diameter of the cylinder = 14cm
Radius of the cylinder = 14 / 2 = 7cm
Height of the cylinder = 10cm

Total surface area of the cylinder = 2 * pie * r * h + 2 * pie * r²
= 2 * 22 / 7 * 7 * 10 + 2 * 22 / 7 * 7 * 7
= 440 + 308
= 748 sq cm

Hence, the total surface area of the cylinder is 748 sq cm.
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Q.4) In a building, there are 24 cylindrical pillars. The radius of each pillar is 28cm and its height is 4m. Find the cost of painting the curved surface area of all pillars at the rate of Rs. 10 per sq m.

SOLUTION:

Given:
Radius of a pillar = 28cm = 0.28m
Height of a pillar = 4m

Curved surface area of a pillar = 2 * pie * r * h
= 2 * 22 / 7 * 0.28 * 4
= 7.04 sq m

Curved surface area of 24 pillars = 7.04 * 24 = 168.96 sq m
As the rate of painting = RS. 10 per sq m
Total cost of painting = Rs. 10 * 168.96 = Rs. 1,689.60

Hence, the cost of painting the curved surface area of all pillars is Rs. 1,689.60
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Q.5) It costs Rs. 2,200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the rate of painting is Rs. 20 per sq, find :
(a) the inner curved surface area of the vessel
(b) the radius of the base

SOLUTION :

Given:
(a) total cost of painting = Rs. 2,200 and rate of painting = Rs. 20 per sq m

Area of inner curved surface = Total cost of painting / Rate of painting = 2,200 / 2 = 110 sq m

(b) Depth of the vessel = 10m [ Given ]
Let r be the radius of the base of the cylindrical vessel

Then its curved surface area = 110m²
= 2* pie * r * h = 110m²
= 2 * 22 / 7 * r * 10 = 110m²
= r = 110 * 7 / 2* 22 * 10 = 7 / 4
= 1.75m

Hence, the radius of the base of the cylindrical vessel is 1.75m.
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