Gaur Classes

Class Test – Mathematics (Class IX)
Chapter – 11: Surface Areas and Volumes (Cone, Sphere & Hemisphere)

Maximum Marks: 40 Time: 1½ Hours

Section – A (1 × 4 = 4 marks)

(2 MCQs + 2 Fill in the Blanks)

Q1. The curved surface area of a cone is given by:
(a) πr² (b) πrl (c) 2πr² (d) πr(h + l)

Q2. If the radius of a sphere is doubled, then its surface area becomes —
(a) 2 times (b) 3 times (c) 4 times (d) 8 times

Q3. Fill in the blank:
The volume of a hemisphere of radius r is ___________.

Q4. Fill in the blank:
The total surface area of a cone = πr(l + r), where l is the __________ of the cone.

Section – B (2 × 4 = 8 marks)

(Short Answer Questions – 2 marks each)

Q5. Find the curved surface area of a cone of radius 7 cm and slant height 24 cm.

Q6. A hemisphere bowl of radius 10.5 cm is painted from outside. Find the area painted.

Q7. Find the radius of a sphere whose surface area is 616 cm².

Q8. A cone of height 24 cm and radius 7 cm is melted to form a sphere. Find the radius of the sphere formed.

Section – C (4 × 2 = 8 marks)

(Long Answer Questions – 4 marks each)

Q9. A right circular cone has base radius 3.5 cm and height 12 cm. Find its
(i) slant height,
(ii) curved surface area,
(iii) total surface area, and
(iv) volume.

Q10. The diameter of a sphere is 14 cm. Find its
(i) surface area,
(ii) volume, and
(iii) how many such spheres can be made by melting a cone of base radius 7 cm and height 24 cm.

Section – D (Essay Type – 1 × 8 = 8 marks)

Q11.
A cone, a hemisphere and a cylinder stand on the same base and have the same height of 7 cm.
Find the ratio of their volumes. Also, calculate their total surface areas when the radius of the base is 3.5 cm.
Explain each step clearly and state all formulas used.

Chemistry
Ch - 2 Acids, Bases and Salts

Acids are sour in taste.

Acids turns Blue litmus to Red (ABR).

Bases are bitter in taste.

Bases turns Red litmus to Blue (BRB).

★ Litmus is a natural indicator, turmeric is another such indicator.

We can also use synthetic indicators such as methyl orange and phenolphthalein.

★ Methyl Orange:
Acidic pH – Red orange colour
Basic pH – Yellow colour

★ Phenolphthalein:
Acidic pH – Colourless
Basic pH – Pink

These indicators tells us whether a substance is acidic or basic by change in colour.

★ Olfactory Indicators:
→ There are some substances whose odour (smell) changes in acidic or basic media. eg. vanilla, onion, and clove can be used as olfactory indicators.

Sample Solution | Red Litmus Solution | Blue Litmus Solution | Phenophthalein Solution | Methyl Orange Solution

i) HCl – No change | Red colour | Colourless | Red orange
ii) H₂SO₄ – No change | Red colour | Colourless | Red orange
iii) HNO₃ – No change | Red colour | Colourless | Red orange
iv) CH₃COOH – No change | Red colour | Colourless | Red orange
v) NaOH – Blue | No change | Pink | Yellow
vi) Ca(OH)₂ – Blue | No change | Pink | Yellow
vii) KOH – Blue | No change | Pink | Yellow
viii) Mg(OH)₂ – Blue | No change | Pink | Yellow
ix) NH₄OH – Blue | No change | Pink | Yellow

* How do Acids and Bases react with Metals?

Acid + Metal → Salt + Hydrogen gas

Base + Metal → Salt + Hydrogen gas

Zn + H₂SO₄ → ZnSO₄ + H₂ (g)
(zinc) (dil. sulphuric acid) (zinc sulphate) (hydrogen gas)

Zn + NaOH → Na₂ZnO₂ + H₂ (g)
(zinc) (sodium hydroxide) (sodium zincate) (hydrogen gas)

Note: Metal in the above 2 reaction displaces hydrogen atoms from the acids or base as hydrogen gas and forms a compound called a "salt".

"Reactions are not possible with all metals."

Reaction of zinc granules with dilute sulphuric acid and testing hydrogen gas by burning.

★ How do Metal carbonates and Metal hydrogen carbonates reacts with acids?

★ Metal carbonate / Metal hydrogen carbonate + Acid → Salt + carbon dioxide + water

Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂

NaHCO₃ + HCl → NaCl + H₂O + CO₂

On passing the carbon dioxide gas evolved through lime water.

Ca(OH)₂ + CO₂ → CaCO₃ (s) + H₂O
(lime water) (white ppt)

On passing excess carbon dioxide the following reaction takes place:

CaCO₃ (s) + H₂O + CO₂ → Ca(HCO₃)₂
(soluble in water)

★ How do Acids and Bases react with each other?

→ Reaction between an Acid & Base to give salt & water is known as neutralisation reaction.

Base + Acid → Salt + Water
NaOH + HCl → NaCl + H₂O

• In this activity we have observed that the effect of a base is nullified by an acid and vice versa.

★ Reaction of Metallic Oxides with Acids:

Metal oxide + Acid → Salt + water
eg.:
CuO + HCl → CuCl₂ + H₂O
(copper oxide) (Hydrochloric acid) (copper chloride) (water)
(Blue green colour)

Colour of the solution becomes blue green and copper oxide dissolves, the blue green colour of the solution due to the formation of copper (II) chloride on the reaction.

Similarly to the reaction of a base with an acid, metallic oxides are said to be basic oxide.

★ Reaction of Non-Metallic Oxides with Base:

→ Ca(OH)₂ + CO₂ → CaCO₃ + H₂O
(calcium hydroxide) (calcium carbonate)
(salt)

Since, this similar to the reaction between base and an acid to give salt and water, we can conclud that non-metallic oxides are acidic in nature.

★ What do all Acids and Bases have in Common?

The bulb will start glowing in the case of acids. But we will observe that Glucose and Alcohol do not conduct electricity. Glowing of bulbs indicates that there is a flow of electric current through the solution.

Acids produce Hydrogen Ions (H⁺[aq]) in solution, which are responsible for their acidic property

★ Strong and weak Acids:

Those acids which are completely ionised in water are called strong acids

Strong acids produce a large amount of Hydrogen ion in aqueous medium.

Hydrochloric acid (HCl), sulphuric acid (H₂SO₄), and Nitric acid (HNO₃) are all strong acids because they are completely ionised in water.

HCl(aq) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq)
HNO₃(aq) + H₂O(l) → H₃O⁺(aq) + NO₃⁻(aq)
H₂SO₄(aq) + H₂O(l) → H₃O⁺(aq) + SO₄²⁻(aq)

Those acids which are partially ionised in water are called weak acids.

Weak acids produce only a small amount of Hydrogen ion in aqueous medium.

for eg.

acetic acid (CH₃COOH), carbonic acid (H₂CO₃), formic acid (HCOOH)

CH₃COOH(aq) + water(H₂O(l)) ⇌ H₃O⁺(aq) + CH₃COO⁻(aq)
H₂CO₃(aq) + 2H₂O(l) ⇌ 2H₃O⁺(aq) + CO₃²⁻(aq)

A double headed arrow indicates incomplete ionisation in case of weak acids.

The relative strength of acid can be compared in terms of degree of dissociation denoted by α.