Question

One day a boy going to home from the school saw a carpenter working on wood. He

found that he is carving out a cone of the same height and same diameter from cylinder.

The height of the cylinder is 2.4 cm and base radius 0.7cm . Whole watching it some

questions came to his mind. Help him to answer the questions ?

1. What is the slant height of the conical cavity so formed

a. 2.5 cm

b. 1.5 cm

c. 3 cm

d. 3.2 cm

2. The curved surface area of cylinder

a. 9.57cm2

b. 10.56cm2

c. 15.5 cm2

d. 13.2 cm2​

Answer 1

Given - Height and base

Find - Slant height and curved surface area

Solution - The slant height of the cone will be a. 2.5 cm and the curved surface area of the cylinder will be b. 10.56 cm².

The slant height of the cone can be calculated through the Pythagoras theorem.

The height of the cylinder will be perpendicular, the radius will be base and the slant height will be the hypotenuse.

So, H² = 2.4² + 0.7²

H² = 5.76 + 0.49

H² = 6.25

H = ✓6.25

H = 2.5 centimetres

Hence, the slant height of the cone will be a. 2.5 cm.

The curved surface area of a cylinder can be calculated by the formula = 2πrh

The curved surface area of the cylinder = 2*π*0.7*2.4

The curved surface area of the cylinder = 10.56 cm².

Hence, the Curved surface area of the cylinder is b. 10.56 cm².

Answer 2

Answer:

1st question  (a)

2nd question (b)

Step-by-step explanation:

Given data  

Carpenter carving a cone of same height and same diameter from cylinder

height of the cylinder h = 2.4 cm

base radius of the cylinder r = 0.7 cm  

here we need to find slant height and curved surface area of the cone  

from given data height of cone = 2.4 cm

 radius of the base of the cone = 0.7 cm

Slant height  of cone

Slant height   $l = \sqrt{r^{2} + h^{2} }$  

                      $l$ = $\sqrt{(2.4)^{2} + (0.7)^{2} }$    

                      $l = \sqrt{5.76 + 0.49 }$  

                      $l = \sqrt{6.25}$  = $\sqrt{(2.5)^{2} }$ = 2.5 cm

⇒ Slant height of the cone = 2.5 cm

Curved surface area of cylinder

curved surface area = 2$\pi$rh

                                 = 2 × $\frac{22}{7}$ × 0.7 × 2.4

                                 = 2 × 22 × 0.1 ×2.4

                                 = 10.56 $cm^{2}$    

⇒ 1 st question (a)

⇒ 2nd question (b)