surface areas and volumes

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere

• 5cm

• 6cm

• 7cm

Answer explanation

6cm

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid

• 200cm2

• 160cm2

• 150cm2

Answer explanation

160cm2

Tags

CCSS.6.G.A.4

Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs 100 per sq. m, find the amount, the associations will have to pay. (Use π = 22/7)

• 7590Rs,

  379500Rs

• 1500Rs

  320000Rs

• 3220Rs

  123455Rs

Answer explanation

cost of 1 tent=7590Rs

total cost =379500Rs

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 5/6 cm³. a)Find the height of the toy.

b)find the cost of painting the hemispherical part of the toy at the rate of ₹10 per cm². [Use π = 22/7]

• 5cm,

  750Rs

• 6cm,

  770Rs

Answer explanation

a)6cm

b)770Rs

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. (Use π = 22/7)

• 4320cm3

• 4000cm3

• 4620cm3

Answer explanation

4620cm3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Two cubes each of volume 27 cm³ are joined end to end to form a solid. Find the surface area of the resulting cuboid.

• 99cm2

• 90cm2

• 9cm2

Answer explanation

90cm2

Tags

CCSS.6.G.A.4

The decorative block is made of two solids-a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere fixed on the-top has a diameter of 4.2 cm. Find the total surface area of the block. [take π = 22/7]

• 163.86cm2

• 162cm2

Answer explanation

163.86cm2

1. Water in a canal, 5.4 𝑚 wide and 1.8 𝑚 deep, is flowing with a speed of 25 𝑘𝑚/h𝑜𝑢𝑟. How much area can it irrigate in 40 minutes, if 10 𝑐𝑚 of standing water is required for irrigation?

• 1600000m2

• 1620000m2

• 16000m2

Answer explanation

1620000m2/162hectare

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

1. If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

• 1:4

• 1:2

• 2:4

Answer explanation

1:4

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

1. The radius and height of a solid right circular cone are in the ratio of 5 ∶ 12. If its volume is 314 𝑐𝑚3, find its total surface area. [Take 𝜋 = 3.14]

• 299.6cm2

• 266.9cm2

Answer explanation

266.9cm2