Mensuration Ex 7.3-10th Std Maths-Book Back Question And Answer
Question 1.
A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is 14 cm and the height of the vessel is 13 cm. Find the capacity of the vessel.
Answer:
Radius of a hemisphere = Radius of the cylinder
Question 2.
Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.
Answer:
Radius of the cone = Radius of the cylinder
r = 32 cm
Height of the cone (H) = 2 cm
Height of the cylinder (h) = 12 – (2 + 2) cm = 8 cm
Volume of the model = Volume of the cylinder + Volume of 2 cones
Question 3.
From a solid cylinder whose height is 2.4 cm and the diameter 1.4 cm, a cone of the same height and same diameter is carved out. Find the volume of the remaining solid to the nearest cm3.
Answer:
Radius of a cylinder = Radius of a cone r = 0.7 cm
Height of a cylinder = Height of a cone (h) = 2.4 cm
Volume of the remaining solid = Volume of the cylinder – Volume of a cone
Volume of the remaining soild = 2.46 cm3
Question 4.
A solid consisting of a right circular cone of height 12 cm and radius 6 cm standing on a hemisphere of radius 6 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is 6 cm and height is 18 cm.
Answer:
Radius of a cone = Radius of a hemisphere = Radius of a cylinder
r = 6 cm
Height of a cone (h) = 12 cm
Volume of the water displaced = Volume of the solid inside = Volume of the cone + Volume of the hemisphere
Volume of water displaced = 905. 14 cm3.
Question 5.
A capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the entire capsule is 12 mm and the diameter of the capsule is 3 mm, how much medicine it can hold?
Answer:
Radius of a hemisphere = Radius of a Cylinder
r = 32 mm = 1.5 mm
Height of the cylinderical portion = 12 mm – (1.5 mm + 1.5 mm) = (12 – 3) mm = 9 mm
Volume of the capsule
Volume of the capsule = 77.8 cu. mm
Question 6.
As shown in figure a cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid.
Answer:
Side of a cube (a) = 7 cm
Radius of a hemisphere (r) = 72 cm
Surface area of the solid = T.S.A of the cube + C.S.A of the hemisphere – Area of the base of the hemisphere
Question 7.
A right circular cylinder just encloses a sphere of radius r units. Calculate
(i) the surface area of the sphere
(ii) the curved surface area of the cylinder
(iii) the ratio of the areas obtained in (i) and (ii).
Answer:
(i) Surface area of sphere = 4πr2 sq. units
Question 8.
A shuttlecock used for playing badminton has the shape of a frustum of a cone is mounted on a hemisphere. The diameters of the frustum are 5 cm and 2 cm. The height of the entire shuttlecock is 7 cm. Find its external surface area.
Answer:
