PSEB Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.7
PSEB Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.7
PSEB 9th Class Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.7
Question 1.
Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm
Question 2.
Find the capacity in litres of a conical vessel with
(i) radius 7 cm, slant height 25 cm
Question 3.
The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use π = 3.14.)
Question 4.
If the volume of a right circular cone of height 9 cm is 48 πcm3, find the diameter of its base.
Question 5.
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kiloliters ?
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 and
(iii) curved surface area of the cone.
(iii) Curved surface area of a cone
= πrl
= 22/7 × 14 × 50 cm2
= 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:
A right circular cone is received when ∆ ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm.
For the cone so obtained, radius r = 5 cm, height h = 12 cm and slant height l = 13 cm.
Volume of the cone obtained
= 1/3 πr2h
= 1/3 × π × 5 × 5 × 12 cm3
= 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:
Now, if ∆ ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 5 cm, again a right circular cone is received.
For the cone so obtained, radiqs r = 12cm; height h = 5 cm and slant height l = 13 cm.
Volume of the cone obtained
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.
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