Question

1) The length of the base diameter of a wooden toy of conical shape is 10 cm. The expenditure for polishing whole surfaces of the toy at the rate of Rs. 2.10 perm² is Rs. 429. Let us calculate the height of the toy. Let us also determine the quantity of wood which is required to make the toy.​

Answer 1

Answer :-

Given :-

• The length of the base diameter of a wooden toy of conical shape is 10 cm. The expenditure for polishing whole surfaces of the toy at the rate of Rs. 2.10 per m² is Rs. 429.

Find Out :-

• The height of the toy.
• The quantity of wood which is required to make the toy.

Solution :-

Radius of base of the wooden toy $\dfrac{10}{2}$

Area of lateral surface = $\dfrac{429}{2.10}$

According to the question,

⇒ πrl = $\dfrac{429}{2.10}$

⇒ $\dfrac{22}{7} \times 5 \times l = \dfrac{429 \times 100}{210}$

⇒ l = $\dfrac{4290}{21} \times \dfrac{7}{22} \times \dfrac{1}{5}$

⇒ l = $\dfrac{130}{10}$

➡ l = 13 cm

Again, to find height,

➛ (l)² = (r)² + (h)²

➛ (13)² = 25 - (h)²

➛ 169 = 25 + (h)²

➛ 169 - 25 = (h)²

➛ 144 = h²

➛ $\sqrt{144}$ = h

➛ 12 = h

➠ h = 12 cm

∴ The height of the toy is 12 cm.

Now, the required quantity of wood which is required to make the toy,

↦ $\dfrac{1}{3}π{r}^{2}h$

↦ $\dfrac{1}{3} \times \dfrac{22}{7} \times 5 \times 5 \times 12$

➟ 314.29 cu.cm

∴ The quantity of wood which is required to make the toy is 314.29 cu.cm.

Answer 2

Answer:

According to the question,

⇒ πrl = \dfrac{429}{2.10}

2.10

429

⇒ \dfrac{22}{7} \times 5 \times l = \dfrac{429 \times 100}{210}

7

22

×5×l=

210

429×100

⇒ l = \dfrac{4290}{21} \times \dfrac{7}{22} \times \dfrac{1}{5}

21

4290

×

22

7

×

5

1

⇒ l = \dfrac{130}{10}

10

130

➡ l = 13 cm

Again, to find height,

➛ (l)² = (r)² + (h)²

➛ (13)² = 25 - (h)²

➛ 169 = 25 + (h)²

➛ 169 - 25 = (h)²

➛ 144 = h²

➛ \sqrt{144}

144

= h

➛ 12 = h

➠ h = 12 cm

∴ The height of the toy is 12 cm.

Now, the required quantity of wood which is required to make the toy,

↦ \dfrac{1}{3}π{r}^{2}h

3

1

πr

2

h

↦ \dfrac{1}{3} \times \dfrac{22}{7} \times 5 \times 5 \times 12

3

1

×

7

22

×5×5×12

➟ 314.29 cu.cm

∴ The quantity of wood which is required to make the toy is 314.29 cu.cm.