Access Answers for SAT Maths Chapter 13 – Surface Areas and Volumes
Exercise: 13.1
1. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting
cuboid.
Answer:
The diagram is given as:
Given,
The Volume (V) of each cube is = 64 cm3
This implies that a3 = 64 cm3
∴ a = 4 cm
Now, the side of the cube = a = 4 cm
Also, the length and breadth of the resulting cuboid will be 4 cm each. While its height will be 8 cm.
So, the surface area of the cuboid = 2(lb+bh+lh)
= 2(8×4+4×4+4×8) cm2
= 2(32+16+32) cm2
= (2×80) cm2 = 160 cm2
2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the
hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the
vessel.
Answer:
The diagram is as follows:
,Now, the given parameters are:
The diameter of the hemisphere = D = 14 cm
The radius of the hemisphere = r = 7 cm
Also, the height of the cylinder = h = (13-7) = 6 cm
And, the radius of the hollow hemisphere = 7 cm
Now, the inner surface area of the vessel = CSA of the cylindrical part + CSA of hemispherical part
(2πrh+2πr2) cm2 = 2πr(h+r) cm2
2×(22/7)×7(6+7) cm2 = 572 cm2
3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The
total height of the toy is 15.5 cm. Find the total surface area of the toy.
Answer:
The diagram is as follows:
Given that the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm
The total height of the toy is given as 15.5 cm.
So, the height of the cone (h) = 15.5-3.5 = 12 cm
,∴ The curved surface area of cone = πrl
(22/7)×(7/2)×(25/2) = 275/2 cm2
Also, the curved surface area of the hemisphere = 2πr 2
2×(22/7)×(7/2)2
= 77 cm2
Now, the Total surface area of the toy = CSA of cone + CSA of hemisphere
= (275/2)+77 cm2
= (275+154)/2 cm2
= 429/2 cm2 = 214.5cm2
So, the total surface area (TSA) of the toy is 214.5cm2
4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the
hemisphere can have? Find the surface area of the solid.
Answer:
It is given that each side of cube is 7 cm. So, the radius will be 7/2 cm.
We know,
The total surface area of solid (TSA) = surface area of cubical block + CSA of hemisphere – Area of
base of hemisphere
∴ TSA of solid = 6×(side)2+2πr2-πr2
= 6×(side)2+πr2
= 6×(7)2+(22/7)×(7/2)×(7/2)
, = (6×49)+(77/2)
= 294+38.5 = 332.5 cm2
So, the surface area of the solid is 332.5 cm2
5. A hemispherical depression is cut out from one face of a cubical wooden block such that the
diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the
remaining solid.
Answer:
The diagram is as follows:
Now, the diameter of hemisphere = Edge of the cube = l
So, the radius of hemisphere = l/2
∴ The total surface area of solid = surface area of cube + CSA of hemisphere – Area of base of
hemisphere
TSA of remaining solid = 6 (edge)2+2πr2-πr2
= 6l2 + πr2
= 6l2+π(l/2)2
= 6l2+πl2/4
= l2/4(24+π) sq. units
6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends.
The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface
area.
Answer:
Two hemisphere and one cylinder are shown in the figure given below.
Exercise: 13.1
1. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting
cuboid.
Answer:
The diagram is given as:
Given,
The Volume (V) of each cube is = 64 cm3
This implies that a3 = 64 cm3
∴ a = 4 cm
Now, the side of the cube = a = 4 cm
Also, the length and breadth of the resulting cuboid will be 4 cm each. While its height will be 8 cm.
So, the surface area of the cuboid = 2(lb+bh+lh)
= 2(8×4+4×4+4×8) cm2
= 2(32+16+32) cm2
= (2×80) cm2 = 160 cm2
2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the
hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the
vessel.
Answer:
The diagram is as follows:
,Now, the given parameters are:
The diameter of the hemisphere = D = 14 cm
The radius of the hemisphere = r = 7 cm
Also, the height of the cylinder = h = (13-7) = 6 cm
And, the radius of the hollow hemisphere = 7 cm
Now, the inner surface area of the vessel = CSA of the cylindrical part + CSA of hemispherical part
(2πrh+2πr2) cm2 = 2πr(h+r) cm2
2×(22/7)×7(6+7) cm2 = 572 cm2
3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The
total height of the toy is 15.5 cm. Find the total surface area of the toy.
Answer:
The diagram is as follows:
Given that the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm
The total height of the toy is given as 15.5 cm.
So, the height of the cone (h) = 15.5-3.5 = 12 cm
,∴ The curved surface area of cone = πrl
(22/7)×(7/2)×(25/2) = 275/2 cm2
Also, the curved surface area of the hemisphere = 2πr 2
2×(22/7)×(7/2)2
= 77 cm2
Now, the Total surface area of the toy = CSA of cone + CSA of hemisphere
= (275/2)+77 cm2
= (275+154)/2 cm2
= 429/2 cm2 = 214.5cm2
So, the total surface area (TSA) of the toy is 214.5cm2
4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the
hemisphere can have? Find the surface area of the solid.
Answer:
It is given that each side of cube is 7 cm. So, the radius will be 7/2 cm.
We know,
The total surface area of solid (TSA) = surface area of cubical block + CSA of hemisphere – Area of
base of hemisphere
∴ TSA of solid = 6×(side)2+2πr2-πr2
= 6×(side)2+πr2
= 6×(7)2+(22/7)×(7/2)×(7/2)
, = (6×49)+(77/2)
= 294+38.5 = 332.5 cm2
So, the surface area of the solid is 332.5 cm2
5. A hemispherical depression is cut out from one face of a cubical wooden block such that the
diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the
remaining solid.
Answer:
The diagram is as follows:
Now, the diameter of hemisphere = Edge of the cube = l
So, the radius of hemisphere = l/2
∴ The total surface area of solid = surface area of cube + CSA of hemisphere – Area of base of
hemisphere
TSA of remaining solid = 6 (edge)2+2πr2-πr2
= 6l2 + πr2
= 6l2+π(l/2)2
= 6l2+πl2/4
= l2/4(24+π) sq. units
6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends.
The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface
area.
Answer:
Two hemisphere and one cylinder are shown in the figure given below.
