Volume and Surface Area with Explanation

Q1. The volume of milk present in a rectangular container is 2.6 cubic meters, and the area of the base of this container is 6500 sq.cm. Find the depth of milk in the container?

Answer- Option B

Explanation-

Volume = (2.6 x 100 x 100 x 100)cu. cm
Depth =

Volume Area of the base

=

2.6x100x100x100 6500

= 4m

Q2. The Ganga is flowing at a speed of 3.5 km/hr if the river is 36 m wide and 1.5 m deep, what is the amount of water that runs into the sea per minute?

Answer- Option A

Explanation-

Length of water column flown in 1 min. =

3.5x1000 60

m =

175 3

Volume flown per minute =

175 3

x36x

3 2

= 3150m³

Q3. The surface area of a cuboid is 88 sq.cm, and its edges are in the ratio 3 : 2 : 3. What is the volume the cuboid?

Answer- Option D

Explanation-

Let the dimensions of the cuboid be x, 2x and 3x

Then, 2(x*2x + 2x*3x + x*3x) = 88

2x² + 6x² + 3x² = 44

11x² = 44

x = 2

Volume of the cuboid = (2*4*6)cm³ = 48cm³

Q4. Paint costs Rs. 36.50 per kg and to cover 16 sq.ft, 1 kg of paint is required. Find the cost to paint the cube from outside having each side of 8 ft?

Answer- Option A

Explanation-

Surface area of the cube = (6x8²)sq. ft = 384 sq. ft

Quantity of paint required =

384 16

kg = 24kg

Cost of painting = Rs. (36.50x24) = Rs. 876

Q5. The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3, what is the ratio of their volumes?

Answer- Option C

Explanation-

Let their radii be 2x, 3x and heights be 5y, 3y

Ratio of their volumes =

π*(2x)2*5y π*(3x)2*3y

=

20 27

Q6. A metallic sheet is of the rectangular shape with dimension 48 cm x 36 cm. From each one of its corners, a square of 8 cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box?

Answer- Option B

Explanation-

In order to make an open box, a square of side 8 cm is cut off from each of the four corners and the flaps are folded up.

Thus, the box will have the following dimensions:

Length = (48 - 8 - 8)cm = 32cm

Breadth = (36 - 8 - 8)cm = 20cm

Height = 8cm

Volume of the box formed = (32x20x8)cm³ = 5120cm³

Q7. How many planks each of which is 2 m long, 2.5 cm broad, and 4 cm thick can be cut off from a wooden block 6 m long, 15 cm broad, and 40 cm thick?

Answer- Option D

Explanation-

Length of wooden block = 6m = 600cm

Breadth of wooden block = 15cm, Height of wooden block = 40cm

Volume of wooden block = (600x15x40)cm³

Length of each plank = 2m = 200cm, Breadth of each plank = 2.5cm and Height of each plank = 4cm

Volume of each plank = (200x2.5x4)cm²

So, number of planks =

Volume of wooden block Volume of each plank

=

600x15x40 200x2.5x4

= 3x15x4 = 180