Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

A bucket is in the shape of the frustum of a right circular cone as shown in figure. Find the curved surface area. (Use $$\pi$$ = $$3$$)

A
$$410$$ $$m^2$$

B
$$439.6$$ $$m^2$$

C
$$400$$ $$m^2$$

D
$$405$$ $$m^2$$

Solution

Curved surface area of frustum $$=\pi (R + r) l$$
Where $$r$$ and $$R$$ is base radius and top radius respectively.
Diameter $$=$$ Radius $$\times 2$$
Radius, $$R = 2.5$$ m, $$r= 1$$ m, $$s= 40$$ m
CSA = $$\pi (2.5 + 1) \times 40$$
$$=\pi (3.5) \times 40$$
$$=3.14 \times 3.5 \times 40$$
CSA $$=439.6 \ m^2$$
Question 2
1 / -0

Find the curved surface area of a frustum cone whose larger and smaller radius is 12 and 8 cm. The slant height is 24 cm. (Use $$\pi$$ = 3.14)

A
1,507.2 cm$$^2$$

B
1,407.2 cm$$^2$$

C
1,307.2 cm$$^2$$

D
1,207.2 cm$$^2$$

Solution

Curved surface area of a frustum cone = $$\pi$$(r + R)s $$\Rightarrow$$ ?
= 3.14 $$\times$$ (8 + 12) $$\times$$ 24
= 3.14 x (20) $$\times$$ 24
Curved surface area of a frustum cone = 1,507.2 cm$$^2$$
Question 3
1 / -0

Fill in the blank: The surface area of a frustum cone is measured in ______ units.

A
Cubic

B
Square

C
Meter

D
Liter

Solution

The surface area of a frustum cone is measured in square units.
Question 4
1 / -0

Calculate the volume of a frustum cone :
Given D = 2 cm, d = 1 cm, h = 15 cm.

A
27.475 $${cm}^3$$

B
25.674 $${cm}^3$$

C
20,976 $${cm}^3$$

D
14.975 $${cm}^3$$

Solution

Volume = $$\displaystyle \frac{\pi h}{3} (R^2 + Rr + r^2)$$
Diameter = radius $$\times 2$$
Radius, R = 1 cm, r = 0.5 cm
= $$\displaystyle \frac{3.14 \times 15}{3} (1^2 + 1 \times 0.5 + 0.5^2)$$
= $$3.14 \times 5(1 + 0.5 + 0.25)$$
= $$3.14 \times 8.75$$
= $$27.475 cm^3$$
Question 5
1 / -0

The curved surface area of a frustum cone is calculated by using the formula,_____________.

A
$$\pi l(R - r)$$

B
$$\pi l(R + r)$$

C
$$\pi l(R \times r)$$

D
$$2\pi l(R + r)$$

Solution

The curved surface area of a frustum cone is calculated by using the formula,
= $$ πl(r+R) $$
where l = slant height of a cone
R = bottom circle radius
r = top circle radius
Question 6
1 / -0

A bucket is in the shape of the frustum of a right circular cone, whose radii are 5 and 10 mm. The curved surface area is $$210$$ mm. Find the slant height. (Use $$\pi$$ = $$3$$)

A
$$1.76$$ mm

B
$$2.6$$ mm

C
$$3.5$$ mm

D
$$4.66$$ mm

Solution

Curved surface area = $$\pi (R + r) l$$
$$210 = \pi (10 + 5) l$$
$$\displaystyle \frac{210}{3 \times 15} = l$$
Slant height, $$l = 4.66 mm$$
Question 7
1 / -0

A bucket is in the shape of the frustum with the top and bottom circle area is $$250$$ and $$150$$ $$m^2$$. The height of the bucket is $$27$$ m. Find the volume.

A
$$2,121.60$$ $$m^3$$

B
$$3,410.15$$ $$m^3$$

C
$$5,342.76$$ $$m^3$$

D
$$4,320.15$$ $$m^3$$

Solution

Volume of the frustum cone = $$\displaystyle \frac{h}{3} [A_1 + A_2 + \sqrt{A_1 A_2}]$$
= $$\displaystyle \frac{h}{3} [250 + 150 + \sqrt{250 \times 150} ]$$
= $$\displaystyle \frac{27}{3} [400 + \sqrt{37,500} ]$$
= $$\displaystyle 9 [400 + 193.64 ]$$
$$= 5,342.76$$ $$m^3$$
Question 8
1 / -0

What is the capacity of a bucket which if $$45$$ cm high if its radii at the ends are $$28$$ cm and $$7$$ cm?

A
$$48490.5$$ cm$$^3$$

B
$$5622.5$$ cm$$^3$$

C
$$4522.5$$ cm$$^3$$

D
None of these

Solution

R.E.F image
$$ V = \dfrac{\pi }{3}h(R^{2}+r^{2}+Rr) $$
$$ \Rightarrow V = \dfrac{\pi }{3}\times 45 [28^{2}+7^{2}+28\times 7]\Rightarrow \boxed{V = 48490.5} $$
Question 9
1 / -0

If the radii of the circular ends of a conical glass are $$15$$ and $$9$$ cm whose slant height is 35 cm. Find the surface area of the glass? (Use $$\pi$$ = $$3$$)

A
$$2420$$ $$cm^2$$

B
$$2520$$ $$cm^2$$

C
$$2220$$ $$cm^2$$

D
$$2120$$ $$cm^2$$

Solution

Curved surface area = $$\pi ( R + r) l$$
= $$3 \times (15 + 9) \times 35$$
= $$3 \times 24 \times 35$$
$$= 2520$$ $$cm^2$$
Question 10
1 / -0

A vessel is in the form of a frustum of a cone. The area of the ends of the frustum cone are $$122$$ $$cm^2$$ and $$205$$ $$cm^2$$. If the curved surface area is $$305$$ $$cm^2$$. Find the total surface area.

A
$$613$$ $$cm^2$$

B
$$632$$ $$cm^2$$

C
$$620$$ $$cm^2$$

D
$$640$$ $$cm^2$$

Solution

Total surface area = $$\pi (R + r) s + \pi R^2 + \pi r^2$$
$$= 305 + 122 + 205$$
$$= 632 cm^2$$

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 16

Result

Surface Areas and Volumes Test - 16

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SHARING IS CARING

Question 1

$$410$$ $$m^2$$

$$439.6$$ $$m^2$$

$$400$$ $$m^2$$

$$405$$ $$m^2$$

Solution

Question 2

1,507.2 cm$$^2$$

1,407.2 cm$$^2$$

1,307.2 cm$$^2$$

1,207.2 cm$$^2$$

Solution

Question 3

Cubic

Square

Meter

Liter

Solution

Question 4

27.475 $${cm}^3$$

25.674 $${cm}^3$$

20,976 $${cm}^3$$

14.975 $${cm}^3$$

Solution

Question 5

$$\pi l(R - r)$$

$$\pi l(R + r)$$

$$\pi l(R \times r)$$

$$2\pi l(R + r)$$

Solution

Question 6

$$1.76$$ mm

$$2.6$$ mm

$$3.5$$ mm

$$4.66$$ mm

Solution

Question 7

$$2,121.60$$ $$m^3$$

$$3,410.15$$ $$m^3$$

$$5,342.76$$ $$m^3$$

$$4,320.15$$ $$m^3$$

Solution

Question 8

$$48490.5$$ cm$$^3$$

$$5622.5$$ cm$$^3$$

$$4522.5$$ cm$$^3$$

None of these

Solution

Question 9

$$2420$$ $$cm^2$$

$$2520$$ $$cm^2$$

$$2220$$ $$cm^2$$

$$2120$$ $$cm^2$$

Solution

Question 10

$$613$$ $$cm^2$$

$$632$$ $$cm^2$$

$$620$$ $$cm^2$$

$$640$$ $$cm^2$$

Solution

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