**NCERT Maths Specific Questions Of Mensuration for 9 and 10** grade

**Mensuration** is the part of **mathematics** that was born in the lap of geometry in which we study physical quantity like **area, volume, perimeter** and another related quantity of all kinds of geometrical figures. **The questions of mensuration** obligatorily are a piece of the **maths** study material of each class and the **questions of mensuration** are likewise asked in each competitive exam additionally so this post of Future Study Point is helpful for everyone. **Mensuration** is ordered into two sections (i) Two-dimensional geometrical figure (ii) Three-dimensional geometrical figure, here we will study specific questions of mensuration for which students commonly required assistance from his mentor or educator. These are the specific questions of mensuration that are posed in the CBSE board exam and in the competitive exams. We trust you will get support from the way of solutions for illuminating the questions. Questions are clarified through a step-by-step way by a specialist in maths so that everyone could comprehend the way of solution.

This post consists of a few examples with the solutions and some of the unsolved questions which are taken from the NCERT and different maths CBSE guides.

**NCERT Solutions Class 10 Science from chapter 1 to 16**

**Example(1)-Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4 for 1000 cm ^{2}, find the cost of cardboard required for supplying 250 boxes of each kind.**

Ans.

We have to determine total cost of cardboard required to supply 250 boxes of each type

The cardboard required to prepare bigger box = TSA of box + 5% of TSA of the box

TSA of box = 2(lb + bh + hl) = 2(25×20 + 20 × 5 + 5×25)

⇒2×(500 + 100 + 125) = 2 ×725 =14 50 sq.cm

Additional cardboard is required to buid the box = 5 % of 1450 =5/100 ×(1450)=72.5

Cardboard required to build bigger box = 1450 + 72.5 =1522 .5 sq.cm

Cardboard required for 250 bigger boxes = 250× 1522.5 = 380625

Therefore 380625 sq.cm cardboard is required to prepare 250 bigger boxes

TSA of small box of the dimension = 2(15×12 + 12×5 + 15× 5) = 2 ×(180 + 60 +75) = 2×315= 630 sq.cm

Additional cardboard is required to build smaller box = 5% of 630 = 5/100 ×(630) = 31.5 sq.cm

Cardboard required to build this box = 630 + 31.5 = 661.5 sq.cm

Cardboard required for 250 smaller boxes = 250× 661.5 = 165375

Therefore 165375 sq.cm cardboard is required to prepare 250 boxes

Cardboard required to prepare 250 boxes of both kinds = 380625 + 165375 = 546000 sq.cm

The cost of 1000 sq.cm cardboard is = Rs 4

Cost of 546000 sq.cm cardboard will be

Therefore the cost of cardboard required to prepare 250 boxes of each type is Rs 2184

**Example 2- A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm andlength is 1 m.**

Answer.

The length of road roller(h) = 1 m

The diameter of road roller = 84 cm

Its radius = 42 cm

The area occupied by it on the road in one revolution = The curved surface area of the road = 2πrh

Therefore area occupied by it on the road in one revolution =2.64 sq.m

In 750 revolution the whole of the road is covered

In 750 revolution the roller will cover the area

=2.64 × 750=1980

Therefore the area of road = 1980 sq.m

**Example 3. A cubical block of the side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of solid.**

Ans. The greatest diameter of the hemisphere surmounted on one of the face of a cube is the side of the cube

The side of the cube = 7 cm

The surface area of solid =TSA of cube + CSA of hemisphere –area of the circular base of the hemisphere

⇒ 6a² + 2πr² – πr²= 6a² + πr²

a = 7 cm, r = 7/2 = 3.5 cm

⇒ 6 × a² + π ×r²

= 294 + 38.5

= 332.5

The surface area of solid = 332.5 sq.cm

**Q4.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends(see fig.). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.**

Ans. The length of the entire capsule = 14 mm

The diameter of the capsule = 5 mm

Radius of the capsule = 2.5 mm

The length of the cylindrical part of the capsule = 14 –(2.5 + 2.5) = 9 mm

The surface area of capsule = The curved surface area of its cylindrical part + curved surface area of its two hemispherical ends

⇒ 2πrh + 2×2πr²

=2πr(h +2r)

Therefore 220 sq.mm is the entire surface area of the capsule

**Q5.A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with a length 5 cm and a diameter of 2.8 cm.**

Ans.

The length of gulab jamun = 5 cm

The length of its cylindrical part (h) = 5 –(1.4 + 1.4) =5 –2.8=2.2

Therefore the length(h) of cylindrical part is 2.2 cm

Diameter of gulam jamun = 2.8 cm

Radius of gulab jamun = 2.8/2 = 1.4 cm

Volume of gulab jamun(V) = Volume of cylinderical part + Volume of two hemispherical part

45 gulab jamun contain sugar syrup 30 % of 1127.28

= .30 ×1127.28 = 338.184 ≈ 338

Therefore 338 cubic.cm sugar syrup contained in 45 gulab jamun.

**Q6.A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see figure)**

Ans. The volume of wood in the pen stand = Volume of the wooden cuboid – Volume of 4 depressions

The volume of the wooden cuboid = l × b × h

l = 15 cm, b = 10 cm, h = 3.5 cm

⇒The volume of the wooden cuboid = 15 × 10 × 3.5 = 525 cubic.cm

The volume of 4 conical depression of each of radius(r) 0.5 cm and height(h) 1.4 cm

= 1.47

∴ The volume of wood in the pen stand = 525 – 1.47 =523.53

Therefore 523.53 cubic.cm is the volume of wood in the pen stand

**Solve the following important questions generally asked in the CBSE board exams and competitive entrance exams.**

Q1. The water is flowing within a circular pipe of diameter 1.4 cm at the speed of 1.8 km/h, how much time it will take to fill a cuboidal tank of 30000 liters.

Q2. A solid metallic sphere of the diameter of 16 cm is melted and recast into spherical bullets, how many bullets can be formed of the diameter 4 mm.

Q3. A solid metallic cylinder of the diameter 40 cm and height 50 cm is melted and recast into a wire of 4 mm diameter, find the length of wire so formed.

Q4. What will be the ratio of radius and height of a circular cylinder if its volume and radius is equal to the volume and radius of a sphere?

Q5. If the ratio of the volume of two-sphere is 27: 64, find the ratio between their surface areas.

Q6. The level of water in a cylindrical vessel of the 9 cm is raised by 12 cm when a certain ball is dropped inside it and submerged completely, finds the diameter of the ball.

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