"Othello" written by William Shakespeare play explores themes of jealousy, manipulation, betrayal

Volume of a right circular cone (Exercise: 13.7, Sums 6 to 9)

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.