Surface Area And Volume Test

Result

Surface Area And Volume Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Anju has used cloth on edges of a rectangular aquarium to make it look fancy. The length of the aquarium is 60 cm, whereas the width and height are 50 cm each.

(i) What is the total surface area of the aquarium?
(ii) How much length of cloth is used on all edges?

A
(i) 15,000 cm²
(ii) 610 cm

B
(i) 16,000 cm²
(ii) 630 cm

C
(i) 17,000 cm²
(ii) 640 cm

D
(i) 18,000 cm²
(ii) 650 cm

Solution

Here, l = 60 cm, b = 50 cm, h = 50 cm

(i) Total surface area of the aquarium = 2(lb + bh + hl)
= 2(60 × 50 + 50 × 50 + 50 × 60) cm²

= 2(3000 + 2500 + 3000) cm²
= 2 × 8500 cm² = 17,000 cm²
Hence, total surface area of the aquarium = 17,000 cm²

(ii) A cuboid has 12 edges. These consist of 4 lengths, 4 breadths and 4 heights.
∴ Length of the cloth required = 4l + 4b + 4h

= (4 × 60 + 4 × 50 + 4 × 50) cm
= (240 + 200 + 200) cm = 640 cm
Question 2
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The volume of a cylinder is 5184 cm³. A cone of radius and height same as those of cylinder is carved out of it. The cone is then melted to form a cube and then cut into two equal cuboids. Both the small cuboids are then plated gold at the cost of Rs. 2.50 per cm². Find the total cost of gold plating.

A
Rs. 2880

B
Rs. 2740

C
Rs. 2625

D
Rs. 2500

Solution

Volume of a cylinder is 3 times the volume of a cone having same radius and height.
Thus, volume of the given cone = 5184 ÷ 3 = 1728 cm³

Volume of the cube = Volume of the cone

Let the side of cube be x cm.
x³ = 1728
x = 12 cm

If the cube is cut into two cuboids, dimensions of each part would be 12 cm, 12 cm and 6 cm.

Surface area of each small cuboid = 2(lb + bh + hl) = 2(12 × 12 + 12 × 6 + 12 × 6) = 2 (144 + 72 + 72) = 576 cm²

Surface area of two cuboids = 576 × 2 = 1152 cm²
Total cost of gold plating = 1152 × 2.5 = Rs. 2880