Updated By SaraNextGen

On March 11, 2024, 11:35 AM

Question 1:

Find the volume of the right circular cone with

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

Answer:

(i) Radius (r) of cone = 6 cm

Height (h) of cone = 7 cm

Volume of cone

Therefore, the volume of the cone is 264 cm³.

(ii) Radius (r) of cone = 3.5 cm

Height (h) of cone = 12 cm

Volume of cone

Therefore, the volume of the cone is 154 cm³.

Question 2:

Find the capacity in litres of a conical vessel with

(i) radius 7 cm, slant height 25 cm

(ii) height 12 cm, slant height 13 cm

Answer:

(i) Radius (r) of cone = 7 cm

Slant height (l) of cone = 25 cm

Height (h) of cone 

Volume of cone

Therefore, capacity of the conical vessel

=  

= 1.232 litres

(ii) Height (h) of cone = 12 cm

Slant height (l) of cone = 13 cm

Radius (r) of cone 

Volume of cone 

Therefore, capacity of the conical vessel

=  

= litres

Question 3:

The height of a cone is 15 cm. If its volume is 1570 cm³, find the diameter of its base. [Use π = 3.14]

Answer:

Height (h) of cone = 15 cm

Let the radius of the cone be r.

Volume of cone = 1570 cm³

⇒ r = 10 cm

Therefore, the diameter of the base of cone is

10×2=20 cm.

Question 4:

If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.

Answer:

Height (h) of cone = 9 cm

Let the radius of the cone be r.

Volume of cone = 48π cm³

Diameter of base = 2r = 8 cm

Question 5:

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres? 

Answer:

Radius (r) of pit 

Height (h) of pit = Depth of pit = 12 m

Volume of pit 

= 38.5 m³

Thus, capacity of the pit = (38.5 × 1) kilolitres = 38.5 kilolitres

Question 6:

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone

Answer:

(i) Radius of cone = 

Let the height of the cone be h.

Volume of cone = 9856 cm³

h = 48 cm

Therefore, the height of the cone is 48 cm.

(ii) Slant height (l) of cone 

Therefore, the slant height of the cone is 50 cm.

(iii) CSA of cone = πrl

= 2200 cm²

Therefore, the curved surface area of the cone is 2200 cm².

Question 7:

A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Answer:

When right-angled ΔABC is revolved about its side 12 cm, a cone with height (h) as 12 cm, radius (r) as 5 cm, and slant height (l) 13 cm will be formed.

Volume of cone 

= 100π cm³

Therefore, the volume of the cone so formed is 100π cm³.

Question 8:

If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Answer:

When right-angled ΔABC is revolved about its side 5 cm, a cone will be formed having radius (r) as 12 cm, height (h) as 5 cm, and slant height (l) as 13 cm.

Volume of cone 

Therefore, the volume of the cone so formed is 240π cm³.

Required ratio

Question 9:

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Answer:

Radius (r) of heap 

Height (h) of heap = 3 m

Volume of heap

Therefore, the volume of the heap of wheat is 86.625 m³.

Area of canvas required = CSA of cone

Therefore, 99.825 m² canvas will be required to protect the heap from rain.